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Bayesian inference provides a probabilistic reasoning process for drawing conclusions based on imprecise and uncertain data that has been successful in many applications within robotics and information processing, but is most often considered in terms of data analysis rather than synthesis of behaviours. This paper presents the use of Bayesian inference as a means by which to perform Boolean operations in a logic programme while incorporating and propagating uncertainty information through logic operations by inference. Boolean logic operations are implemented in a Bayesian network of Bernoulli random variables with tensor-based discrete distributions to enable probabilistic hybrid logic programming of a robot. This enables Bayesian inference operations to coexist with Boolean logic in a unified system while retaining the ability to capture uncertainty by means of discrete probability distributions. Using a discrete Bayesian network with both Boolean and Bayesian elements, the proposed methodology is applied to navigate a mobile robot using hybrid Bayesian and Boolean operations to illustrate how this new approach improves robotic performance by inclusion of uncertainty without increasing the number of logic elements required. As any logical system could be programmed in this manner to integrate uncertainty into decision-making, this methodology can benefit a wide range of applications that use discrete or probabilistic logic. [ABSTRACT FROM AUTHOR]

Distributed computing supports large scale and data-intensive computations with the cooperation of a multitude of parties, each responsible for a portion of the workload. Such parties are often not fully reliable and may return incorrect results. In this article, we address the problem of assessing the integrity of the computation results. We provide a comprehensive characterization of two techniques, sentinels and twins, evaluating their effectiveness and synergy. Sentinels are pre-computed tasks whose result is known apriori, and enable checking returned results against a ground truth. Twins are replicated tasks assigned to different workers, and enable cross-checking returned results for a same task. The analysis considers many questions that arise in the design of a concrete integrity assessment strategy and identifies the parameters that have a critical impact on the overall protection. Our model enables to tune the integrity controls so to achieve best effectiveness. The model can be applied to a variety of scenarios and offers guidelines that can find extensive application. [ABSTRACT FROM AUTHOR]

Cyber risk affects all organizations. Cyber risk management has generally been based on the heuristics and the availability of protective tools, such as firewalls and passwords. Only recently have there been quantitative analyses of these tools’ costs and benefits. This article presents a probabilistic method based on the existing data in an organization and on their extension to assess the probabilities of new attack scenarios. The objective is to set priorities among risk management measures and to optimize the allocation of limited resources. The model is illustrated first by a statistical analysis of 60 000 incidents, such as lost or stolen laptops, over six years in a specific organization. This analysis is then expanded to the probabilistic domain to cover threats that have not occurred yet. This requires a systematic construction of new attack scenarios and an assessment both of their probability of success and of subsequent losses. The conjunction of statistics and probabilities of more extreme scenarios yields full risk curves. These curves represent the overall cyber risk for the organization and its insurers and unable assessment of the benefits of a spectrum of protective options. [ABSTRACT FROM AUTHOR]

Free-form surface reconstruction using point clouds is a common issue in manufacturing. In this article, a robust joint registration approach for multiview point clouds is proposed to address the problems brought by coarse initialization, outliers, and noise. The basic idea is that minimizing the L2 distance between probability distributions of integrated and standard models, such that a robust initialization is provided for fine registration to avoid local minima. The fine registration is formulated as a joint closet point problem, which is implicitly constrained by closed-loop consistency. In addition, a Lie algebra solution is derived to enforce rigid transformations. The robust initialization is judged by the simulated annealing algorithm. Finally, a probabilistic distance is defined and a maximum likelihood estimation of multiview transformations is designed to resist noise. The experiment on simulated and real data illustrate better robustness of our method to initial errors, outliers, and noise. [ABSTRACT FROM AUTHOR]

Although the GPS-based positioning is ubiquitous for its high precision, the high power consumption brought by the high sampling frequency and the poor GPS signal penetration limits its availability in locating low-power mobile devices (especially mobile phones). As a promising complement, the cellular-based positioning has attracted great attention since it consumes much less power as well as its higher availability. However, the sparsity of cellular-based data (due to lower sampling rate) and large localization errors make the measurement accuracy becomes the main challenge of the cellular-based positioning. hidden Markov model can well solve the problem of positioning error of GPS data, but it is less accurate when applied to map matching of cellular-base data. Therefore, to improve accuracy, in this article, we propose a novel algorithm called the tailored hidden Markov model (THMM) that is optimized for the cellular-based data. Specifically, the geometric, the topological, and the probabilistic characteristics have been considered and fully exploited in the THMM design. Our proposed schemes are evaluated using real-world motor vehicle movement trajectories collected in Tianjin and the experimental results are encouraging compared with the state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

How can we assess a network's ability to maintain its functionality under attacks? Network robustness has been studied extensively in the case of deterministic networks. However, applications such as online information diffusion and the behavior of networked public raise a question of robustness in probabilistic networks. We propose three novel robustness measures for networks hosting a diffusion under the Independent Cascade or Linear Threshold model, susceptible to attacks by an adversarial attacker who disables nodes. The outcome of such a process depends on the selection of its initiators, or seeds, by the seeder, as well as on two factors outside the seeder's discretion: the attacker's strategy and the probabilistic diffusion outcome. We consider three levels of seeder awareness regarding these two uncontrolled factors, and evaluate the network's viability aggregated over all possible extents of an attack. We introduce novel algorithms from building blocks found in previous works to evaluate the proposed measures. A thorough experimental study with synthetic and real, scale-free and homogeneous networks establishes that these algorithms are effective and efficient, while the proposed measures highlight differences among networks in terms of robustness and the surprise they furnish when attacked. Last, we devise a new measure of diffusion entropy, and devise ways to enhance the robustness of probabilistic networks. [ABSTRACT FROM AUTHOR]

We establish the undecidability of conditional affine information inequalities, the undecidability of the conditional independence implication problem with a constraint that one random variable is binary, and the undecidability of the problem of deciding whether the intersection of the entropic region and a given affine subspace is empty. This is a step towards the conjecture on the undecidability of conditional independence implication. The undecidability is proved via a reduction from the periodic tiling problem (a variant of the domino problem). Hence, one can construct examples of the aforementioned problems that are independent of ZFC (assuming ZFC is consistent). [ABSTRACT FROM AUTHOR]

Good responsiveness of autonomous vehicle computing systems is crucial to safety and performance of the vehicles. For example, an autonomous vehicle (AV) may cause an accident if the end-to-end latency from sensing a pedestrian to emergency stop is too high. However, the AV software stacks are too complex to probabilistically analye the end-to-end latency on a multi-core system. They consist of a graph of tasks with different periods, and have a large variability in the task execution times, which may lead to the maximum core utilization $U^{\max }$ U max greater than 1.0 on some cores. This paper proposes a novel stochastic analysis of the end-to-end latency over the AV stacks that allows $U^{\max }$ U max to exceed 1.0 on each core. The proposed analysis models the entire stack as a graph of task graphs under a multi-core partitioned scheduling and provides a probabilistic guarantee that the analyzed latency distribution upper-bounds the one observed from a real system under the assumption of independent task execution times. Using the Autoware stack with inter-task dependent execution times, it is shown that our analysis, combined with a task grouping to mitigate the inter-task correlations, can give a latency distribution for each task path that almost upper-bounds the observed one. [ABSTRACT FROM AUTHOR]

Identifying drug-target interactions has been a key step in drug discovery. Many computational methods have been proposed to directly determine whether drugs and targets can interact or not. Drug-target binding affinity is another type of data which could show the strength of the binding interaction between a drug and a target. However, it is more challenging to predict drug-target binding affinity, and thus a very few studies follow this line. In our work, we propose a novel co-regularized variational autoencoders (Co-VAE) to predict drug-target binding affinity based on drug structures and target sequences. The Co-VAE model consists of two VAEs for generating drug SMILES strings and target sequences, respectively, and a co-regularization part for generating the binding affinities. We theoretically prove that the Co-VAE model is to maximize the lower bound of the joint likelihood of drug, protein and their affinity. The Co-VAE could predict drug-target affinity and generate new drugs which share similar targets with the input drugs. The experimental results on two datasets show that the Co-VAE could predict drug-target affinity better than existing affinity prediction methods such as DeepDTA and DeepAffinity, and could generate more new valid drugs than existing methods such as GAN and VAE. [ABSTRACT FROM AUTHOR]

We propose a novel semi-supervised learning (SSL) assumption—the high separation probability (HSP) assumption—that is complementary to the common low density separation (LDS) assumption, and a highly accurate and efficient SSL algorithm, the transductive minimax probability machine (TMPM). Under the HSP assumption, a preferred classifier should ensure that with high probability the samples are far away from the decision boundary. Similarly, the LDS assumption states that the decision boundary should lie in a low-density region. A remarkable property of HSP is that it provides an elegant theoretical framework for analyzing the generalization performance of SSL, while it remains difficult for the LDS assumption to have a quantitative criterion on how it fits the data. Moreover, it has the same paradigm as the minimax probability machine (MPM) and yields an intractable mixed-integer optimization for solving the transductive label assignment problem. Consequently, we propose TMPM with a label-switching strategy and iterative manner to formalize our approximate solution. Theoretically, we analyze the computational complexity, convergence property, and generalization error bound of TMPM. Empirically, we show that TMPM achieves competitive performance on a wide range of datasets, while being almost one order of magnitude faster than existing SSL approaches. [ABSTRACT FROM AUTHOR]

Robot motion planning methods based on trajectory optimization can efficiently generate feasible and optimal trajectories by minimizing a suitable cost function, even in high-dimensional spaces. However, the main drawback of these methods lies in their proneness to infeasible local minima, especially in complex environments. To mitigate this issue, we propose a novel motion planning method that represents trajectories as samples from a mixture of continuous-time Gaussian processes (MGP) and employs stochastic optimization in order to update the MGP parameters in a cost-minimizing manner. The contributions of the proposed trajectory optimization method arise from the introduced mixture representation and stochastic gradient estimation, dominantly enabling better exploration of the trajectory space and including nondifferentiable optimizing costs. We evaluated the proposed method in multiple simulation benchmarks featuring 7 degree-of-freedom (DOF) robot arms and a 10DOF mobile manipulator. We also conducted a real-world experiment with a 14DOF dual-arm robot. The experimental results demonstrated that the proposed method achieves higher success rate than several state-of-the-art methods, while the advantages stemming from MGPs and stochastic optimization, like trajectory smoothness, support of nondifferentiable cost functions, multiple trajectory solutions, and the ability to tackle high-dimensional planning problems, are inherently kept. [ABSTRACT FROM AUTHOR]

Information about the interruption probability of sensitive industrial processes is important for devising mitigation strategies against voltage sags. However, the existing method for assessing interruption probability is less practical, owing to the difficulty in collecting technical information and data from industrial users. This study proposes a low-data-dependence assessment method for the interruption probability of an industrial process. First, it establishes a general assessment model for the tripping probability of sensitive equipment. Second, it proposes a parameter estimation method to determine the probability density function of the voltage tolerance curve of sensitive equipment in the uncertainty region, according to the equipment trip information recorded by the user. This improves the accuracy of the assessment. Third, this study establishes the logic function expression form of the industrial process structure to describe the relationship between the process interruption probability and the equipment tripping probability. Finally, it proposes a solution method for the process interruption probability based on a heuristic search algorithm, which overcomes the problem of technological process information acquisition, such as the logical relationship among various equipment in the industrial process. The rationality and applicability of the proposed method are verified through a case study. [ABSTRACT FROM AUTHOR]

Deep learning (DL) has demonstrated great potential in solving nonlinear electromagnetic inverse scattering (EMIS) problems. However, the lack of uncertainty quantification and reliability assessment in the predictions remains an unresolved challenge. Overcoming this challenge is of critical importance in practice because of the presence of uncertainties and noise in the measurement data and the ill-posedness of EMIS problems. Here, we propose a conditional renormalization and generation-flow (cRG-Flow) network, a reversible hierarchical network, and develop a novel probabilistic DL strategy to quantify the uncertainty in DL solutions of EMIS problems. The proposed strategy provides two other important advantages over the existing DL approaches for solving EMIS problems. First, due to the reversible property of cRG-Flow, both the forward EM scattering computation and its inverse procedure can be considered simultaneously in the network and, as a result, physical constraints on the DL solutions can be easily imposed. Second, the interpretability of DL solutions is facilitated due to the utilization of RG-Flow. Illustrative examples are provided to demonstrate the performance gain in terms of reconstruction quality and robustness. The proposed method may pave a new avenue for addressing the EMIS problems based on DL schemes with improved reliability and interpretability. [ABSTRACT FROM AUTHOR]

An optimal static voltage stability margin (SVSM) control model considering the uncertain wind farm output is proposed, in which the probability distribution of SVSM is required to satisfy the chance and variance constraints. A probabilistic distribution control method is proposed to solve the model. First, a linear weighted sum of B-spline basic functions is introduced to approximate the analytical function between the probability density function (PDF) of SVSM and control variables. Next, the analytical expression of the PDF of SVSM corresponding to a control variables’ sample is derived, and the sample of corresponding B-spline function weights is obtained, thus forming a series of ‘control variables-weights’ samples. Then, the analytic functions between weights and control variables are obtained using the generated samples to train a radial basis function neural-network, and the analytical function between the PDF of SVSM and control variables is obtained. After that, the chance and variance constraints are transformed into general nonlinear constraints with respect to control variables. Moreover, a method of selecting key control variables by calculating sensitivities is proposed to increase computational efficiency. Test results on the IEEE-39 bus system and an actual provincial power grid demonstrate the feasibility and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Accurate solar photovoltaic (PV) generation forecast is critical to the reliable and economic operation of a modern power system. In practice, due to various faulty issues in the sensor, communication, or database system, the historical and online measurement data may not be always complete, and the missing data could dramatically degrade the forecasting model's accuracy. To solve this problem, this paper proposes an integrated missing-data tolerant model for probabilistic PV power generation forecasting. Taking historical PV generations as input, this model is based on a recursive long short-term memory network (Rec-LSTM), which can provide multi-step ahead forecasting of the probability distribution of PV generation. The unobserved input data will be imputed recursively based on the model output at the previous time step. During the training process, the imputations and forecasting values are iteratively updated by the negative log-likelihood loss function. As a salient advantage, this method can deal with data missing scenarios at both offline and online stages. Numerical experiments are conducted on two one-year datasets from Australia and Singapore, respectively. Probabilistic forecasting for both large-scale and small-scale building-level PV power generation is tested at the time resolution of 15 mins. Testing results show the proposed method can achieve superior probabilistic prediction accuracy as well as strong robustness under various data missing scenarios, compared to other state-of-the-art methods. [ABSTRACT FROM AUTHOR]

The focus of few shot learning research has been on the development of meta-learning recently, where a meta-learner is trained on a variety of tasks in hopes of being generalizable to new tasks. Tasks in meta training and meta test are usually assumed to be from the same domain, which would not necessarily hold in real world scenarios. In this paper, we propose variational hyperparameter inference for few-shot learning across domains. Based on an especially successful algorithm named model agnostic meta learning, the proposed variational hyperparameter inference integrates meta learning and variational inference into the optimization of hyperparameters, which enables the meta-learner with adaptivity for generalization across domains. In particular, we choose to learn adaptive hyperparameters including the learning rate and weight decay to avoid the failure in the face of few labeled examples across domain. Moreover, we model hyperparameters as distributions instead of fixed values, which will further enhance the generalization ability by capturing the uncertainty. Extensive experiments are conducted on two benchmark datasets including few shot learning dataset within-domain and across-domain. The results demonstrate that our methods outperforms previous approaches consistently, and comprehensive ablation studies further validate its effectiveness on few shot learning both within domains and across domains. [ABSTRACT FROM AUTHOR]

In this letter, we propose a novel probabilistic repetition scheme for the uplink massive MIMO system with grant-free access. Compared with canonical K-repetition, the proposed scheme is more flexible and covers the K-repetition as a special case. With the consideration of multiple practical factors, including the sporadic arrivals, the short-packet transmissions, probabilistic repetition, and channel estimation error, the reliability and throughput of the proposed probabilistic repetition assisted grant-free access scheme are theoretically analyzed. It is also proved that the optimal transmission probability for reliability maximization exists and can be found through gradient descent method. Simulation results validate the accuracy of our theoretical analysis, and also show that the proposed Optimal Probabilistic Repetition assisted grant-free Access scheme (OPRA) is superior to the popular modern grant-free random access with repetition transmission, that is, irregular repetition slotted ALOHA (IRSA). [ABSTRACT FROM AUTHOR]

Probabilistic power flow (PPF) is pivotal to quantifying the state uncertainties of distribution power systems. However, it is very challenging due to underlying complex correlations among renewable outputs. To address this problem, a graph attention enabled convolutional network (GAECN) is proposed to approximate PPF in this article. Specifically, the graph convolutional layer of GAECN is used to aggregate the correlations among the nodal power injections during the training process. Within this layer, a full self-adaptive graph convolutional operation is proposed to automatically capture and learn the implicit correlation for achieving significantly enhanced accuracy of PPF. This layer is then followed by the convolutional neural network to capture the uncertain generation of renewable energy to achieve the robust computation of system state variable distributions. The simulation results demonstrate the accuracy and efficiency of the proposed method in IEEE 33, PG&E 69-node, 118-node, and practical 76-node distribution systems. [ABSTRACT FROM AUTHOR]

During clinical practice, radiologists often use attributes, e.g., morphological and appearance characteristics of a lesion, to aid disease diagnosis. Effectively modeling attributes as well as all relationships involving attributes could boost the generalization ability and verifiability of medical image diagnosis algorithms. In this paper, we introduce a hybrid neuro-probabilistic reasoning algorithm for verifiable attribute-based medical image diagnosis. There are two parallel branches in our hybrid algorithm, a Bayesian network branch performing probabilistic causal relationship reasoning and a graph convolutional network branch performing more generic relational modeling and reasoning using a feature representation. Tight coupling between these two branches is achieved via a cross-network attention mechanism and the fusion of their classification results. We have successfully applied our hybrid reasoning algorithm to two challenging medical image diagnosis tasks. On the LIDC-IDRI benchmark dataset for benign-malignant classification of pulmonary nodules in CT images, our method achieves a new state-of-the-art accuracy of 95.36% and an AUC of 96.54%. Our method also achieves a 3.24% accuracy improvement on an in-house chest X-ray image dataset for tuberculosis diagnosis. Our ablation study indicates that our hybrid algorithm achieves a much better generalization performance than a pure neural network architecture under very limited training data. [ABSTRACT FROM AUTHOR]

Channel attention mechanisms have been commonly applied in many visual tasks for effective performance improvement. It is able to reinforce the informative channels as well as to suppress the useless channels. Recently, different channel attention modules have been proposed and implemented in various ways. Generally speaking, they are mainly based on convolution and pooling operations. In this paper, we propose Gaussian process embedded channel attention (GPCA) module and further interpret the channel attention schemes in a probabilistic way. The GPCA module intends to model the correlations among the channels, which are assumed to be captured by beta distributed variables. As the beta distribution cannot be integrated into the end-to-end training of convolutional neural networks (CNNs) with a mathematically tractable solution, we utilize an approximation of the beta distribution to solve this problem. To specify, we adapt a Sigmoid-Gaussian approximation, in which the Gaussian distributed variables are transferred into the interval [0,1]. The Gaussian process is then utilized to model the correlations among different channels. In this case, a mathematically tractable solution is derived. The GPCA module can be efficiently implemented and integrated into the end-to-end training of the CNNs. Experimental results demonstrate the promising performance of the proposed GPCA module. Codes are available at https://github.com/PRIS-CV/GPCA. [ABSTRACT FROM AUTHOR]

Most of the existing classification systems assume that the data used is high-quality labeled. However, the labeling process in real-world may inevitably introduce corruptions into labels which can confuse the performances of classifiers. In this paper, based on Broad Learning System (BLS), we propose a novel label noise tolerant method to classify the pattern with corrupted labels. The standard BLS has shown promising efficiency and accuracy in general classification, but its learning process is prone to be affected by the noisy labels. Here, by detailed probabilistic analysis, we first give the reason for lacks of robustness in standard BLS. Then a maximum likelihood estimation-based objective function is derived for robust classification. In addition, a manifold regularization term is integrated to preserve the local geometry of data, which makes the model to be more robust and flexible to learn the output weights. Given some basic assumptions on the approximation errors, the obtained model can be transformed to a graph regularized reweighted BLS problem. The negative effects of noisy labels in data can be inhibited adaptively by assigning reasonable weights. Theoretical analysis and extensive experiments are provided to demonstrate the robustness and effectiveness of the proposed robust BLS model, especially for the case of large amounts of noisy labels. [ABSTRACT FROM AUTHOR]

A class of self-dual quasi-abelian codes of index 2 over any finite field $F$ is introduced. By counting the number of such codes and the number of the codes in this class whose relative minimum weights are small, such codes are proved to be asymptotically good provided −1 is a square in $F$. Moreover, a class of self-orthogonal quasi-abelian codes of index 2 is defined; and such codes always exist. In a way similar to that for self-dual quasi-abelian codes of index 2, it is proved that these self-orthogonal quasi-abelian codes of index 2 are asymptotically good. [ABSTRACT FROM AUTHOR]

We study an important specialization of the general problem of broadcasting on directed acyclic graphs, namely, that of broadcasting on two-dimensional (2D) regular grids. Consider an infinite directed acyclic graph with the form of a 2D regular grid, which has a single source vertex $X$ at layer 0, and $k + 1$ vertices at layer $k \geq 1$ , which are at a distance of $k$ from $X$. Every vertex of the 2D regular grid has outdegree 2, the vertices at the boundary have indegree 1, and all other non-source vertices have indegree 2. At time 0, $X$ is given a uniform random bit. At time $k \geq 1$ , each vertex in layer $k$ receives transmitted bits from its parents in layer $k-1$ , where the bits pass through independent binary symmetric channels with common crossover probability $\delta \in \left({0,\frac {1}{2}}\right)$ during the process of transmission. Then, each vertex at layer $k$ with indegree 2 combines its two input bits using a common deterministic Boolean processing function to produce a single output bit at the vertex. The objective is to recover $X$ with probability of error better than $\frac {1}{2}$ from all vertices at layer $k$ as $k \rightarrow \infty $. Besides their natural interpretation in the context of communication networks, such broadcasting processes can be construed as one-dimensional (1D) probabilistic cellular automata, or discrete-time statistical mechanical spin-flip systems on 1D lattices, with boundary conditions that limit the number of sites at each time $k$ to $k+1$. Inspired by the literature surrounding the “positive rates conjecture” for 1D probabilistic cellular automata, we conjecture that it is impossible to propagate information in a 2D regular grid regardless of the noise level $\delta $ and the choice of common Boolean processing function. In this paper, we make considerable progress towards establishing this conjecture, and prove using ideas from percolation and coding theory that recovery of $X$ is impossible for any $\delta \in \left({0,\frac {1}{2}}\right)$ provided that all vertices with indegree 2 use either AND or XOR for their processing functions. Furthermore, we propose a detailed and general martingale-based approach that establishes the impossibility of recovering $X$ for any $\delta \in \left({0,\frac {1}{2}}\right)$ when all NAND processing functions are used if certain structured supermartingales can be rigorously constructed. We also provide strong numerical evidence for the existence of these supermartingales by computing several explicit examples for different values of $\delta $ via linear programming. [ABSTRACT FROM AUTHOR]

Data deduplication saves storage space by identifying and removing repeats in the data stream. Compared with traditional compression methods, data deduplication schemes are more computationally efficient and are thus widely used in large scale storage systems. In this paper, we provide an information-theoretic analysis of the performance of deduplication algorithms on data streams in which repeats are not exact. We introduce a source model in which probabilistic substitutions are considered. More precisely, each symbol in a repeated string is substituted with a given edit probability. Deduplication algorithms in both the fixed-length scheme and the variable-length scheme are studied. The fixed-length deduplication algorithm is shown to be unsuitable for the proposed source model as it does not take into account the edit probability. Two modifications are proposed and shown to have performances within a constant factor of optimal for a specific class of source models with the knowledge of model parameters. We also study the conventional variable-length deduplication algorithm and show that as source entropy becomes smaller, the size of the compressed string vanishes relative to the length of the uncompressed string, leading to high compression ratios. [ABSTRACT FROM AUTHOR]

We consider the repair problem for Reed–Solomon (RS) codes, evaluated on an $\mathbb {F}_{q}$ -linear subspace $U\subseteq \mathbb {F}_{q^{m}} $ of dimension $d$ , where $q$ is a prime power, $m$ is a positive integer, and $\mathbb {F}_{q}$ is the Galois field of size $q$. For $q>2$ , we show the existence of a linear repair scheme for the RS code of length $n=q^{d}$ and codimension $q^{s}$ , $s < d$ , evaluated on $U$ , in which each of the $n-1$ surviving nodes transmits only $r$ symbols of $\mathbb {F}_{q}$ , provided that $ms\geq d(m-r)$. For the case $q=2$ , we prove a similar result, with some restrictions on the evaluation linear subspace $U$. Our proof is based on a probabilistic argument, however the result is not merely an existence result; the success probability is fairly large (at least $1/3$) and there is a simple criterion for checking the validity of the randomly chosen linear repair scheme. Our result extend the construction of Dau–Milenkovic to the range $r < m-s$ , for a wide range of parameters. [ABSTRACT FROM AUTHOR]

Let $q\geq 2$ be a prime power. In this paper, we study the distribution of the minimum distance (in the Hamming metric) of a random linear code of dimension $k$ in $\mathbb {F}_{q}^{n}$. We provide quantitative estimates showing that the distribution function of the minimum distance is close (superpolynomially in $n$) to the cumulative distribution function of the minimum of $(q^{k}-1)/(q-1)$ independent binomial random variables with parameters $\frac {1}{q}$ and $n$. The latter, in turn, converges to a Gumbel distribution at integer points when $\frac {k}{n}$ converges to a fixed number in (0, 1). Our result confirms in a strong sense that apart from identification of the weights of proportional codewords, the probabilistic dependencies introduced by the linear structure of the random code, produce a negligible effect on the minimum code weight. As a corollary of the main result, we obtain an improvement of the Gilbert–Varshamov bound for $2< q< 49$. [ABSTRACT FROM AUTHOR]

A unique cognitive capability of humans consists in their ability to acquire new knowledge and skills from a sequence of experiences. Meanwhile, artificial intelligence systems are good at learning only the last given task without being able to remember the databases learnt in the past. We propose a novel lifelong learning methodology by employing a Teacher-Student network framework. While the Student module is trained with a new given database, the Teacher module would remind the Student about the information learnt in the past. The Teacher, implemented by a Generative Adversarial Network (GAN), is trained to preserve and replay past knowledge corresponding to the probabilistic representations of previously learnt databases. Meanwhile, the Student module is implemented by a Variational Autoencoder (VAE) which infers its latent variable representation from both the output of the Teacher module as well as from the newly available database. Moreover, the Student module is trained to capture both continuous and discrete underlying data representations across different domains. The proposed lifelong learning framework is applied in supervised, semi-supervised and unsupervised training. [ABSTRACT FROM AUTHOR]

Change in users’ preferences over time is a challenging issue in collaborative filtering models. Recent temporal recommender systems (RSs) use latent temporal features or probabilistic latent transition models. The models designed using latent temporal features remain confined to point estimation only, i.e., considering single predicted values (e.g., rating) and completely ignore the likelihood of other possible items being generated due to change in users’ preferences. The latent transitive models represent users’ preference over different states using distribution estimation but ignore user–item features. This article proposes an integrated approach for designing collaborative filtering models using both point and distribution estimation techniques together to address this issue. The matrix factorization-based point estimation strategy is applied to integrate user–item correlations and feature information, whereas the hidden Markov model is used for users’ preference distribution over time. Three benchmark datasets were used to evaluate and compare the proposed model’s performance with related state-of-the-art temporal RS models. The proposed model makes the system more robust in handling dynamic users’ preferences. [ABSTRACT FROM AUTHOR]

In this article, we develop an online probabilistic metric-semantic mapping approach for mobile robot teams relying on streaming RGB-D observations. The generated maps contain full continuous distributional information about the geometric surfaces and semantic labels (e.g., chair, table, and wall). Our approach is based on online Gaussian process (GP) training and inference and avoids the complexity of GP classification by regressing a truncated signed distance function (TSDF) of the regions occupied by different semantic classes. Online regression is enabled through a sparse pseudo-point approximation of the GP posterior. To scale to large environments, we further consider spatial domain partitioning via a hierarchical tree structure with overlapping leaves. An extension to a multirobot setting is developed by having each robot execute its own online measurement update and then combine its posterior parameters via local weighted geometric averaging with those of its neighbors. This yields a distributed information processing architecture, in which the GP map estimates of all the robots converge to a common map of the environment while relying only on local one-hop communication. Our experiments demonstrate the effectiveness of the probabilistic metric-semantic mapping technique in 2-D and 3-D environments in both the single- and multirobot settings and in comparison to a deep TSDF neural network approach. [ABSTRACT FROM AUTHOR]

In the past decade, there is an increasing interest in the deployment of unmanned surface vehicles (USVs) for undertaking ocean missions in dynamic, complex maritime environments. The success of these missions largely relies on motion planning algorithms that can generate optimal navigational trajectories to guide a USV. Apart from minimising the distance of a path, when deployed a USVs’ motion planning algorithms also need to consider other constraints such as energy consumption, the affected of ocean currents as well as the fast collision avoidance capability. In this paper, we propose a new algorithm named anisotropic GPMP2 to revolutionise motion planning for USVs based upon the fundamentals of GP (Gaussian process) motion planning (GPMP, or its updated version GPMP2). Firstly, we integrated the anisotropy into GPMP2 to make the generated trajectories follow ocean currents where necessary to reduce energy consumption on resisting ocean currents. Secondly, to further improve the computational speed and trajectory quality, a dynamic fast GP interpolation is integrated in the algorithm. Finally, the new algorithm has been validated on a WAM-V 20 USV in a ROS environment to show the practicability of anisotropic GPMP2. Note to Practitioners—The work reported in this article will be significant for USVs to conduct missions in complex, dynamic maritime environments where various obstacles and time-varying ocean currents exit. We develop this novel motion planning algorithm based on Gaussian process and optimise the trajectory using probabilistic inferences. The new algorithm can generate collision free trajectories that also minimise the influences caused by adverse ocean currents in a highly efficient way. In addition, the planning has been undertaken in a continuous-time domain making the generated trajectory have a guaranteed smoothness and readily feasible for autopilots to track. We use a coastal area with time-varying vortexes to present a challenging practical maritime environment. The presented algorithm integrates the available information about a fluid field regarding energy consumption and hazard level, along with the density of obstacles to plan a navigational route efficiently. To increase the practical performance of the proposed method, diverse models for generating ocean currents need to be developed in the future to tackle unpredictable situations. [ABSTRACT FROM AUTHOR]

Missing data is quite common in the industrial field, resulting in problems in downstream applications, as most data driven methods used in these applications rely on complete and high-quality dataset to build a high-quality model. Existing methods deal with missing data individually regardless of its downstream application, treating all variables equally without considering their different roles in the downstream application. This would affect imputation performance for key variables, thus deteriorating the accuracy of the downstream model. A considerable challenge is how to refine the missing data imputation task. In this paper, a new method termed fine-tuned imputation GAN (FIGAN) is designed to achieve customized data imputation for industrial soft sensor. The major contribution of the paper lies in two aspects: 1) different from the original imputation GAN (GAIN) which treats all variables equally, FIGAN is guided by a soft sensor module so as to achieve customized data imputation by performing improved data imputation on quality-related variables. Enhanced accuracy for the final industrial soft sensor would be possible; 2) in addition, since labels of the soft sensor might also have missing data, a soft sensor with pseudo labeling is designed to conquer the problem with data imputation and label prediction being optimized interactively. Case studies on a converter steelmaking process and a penicillin fermentation process show the feasibility of the proposed FIGAN. It is noted that such customized imputation could be readily transferred to other downstream applications with missing data. Note to Practitioners—Industrial data is often incomplete and needs proper treatment. Meanwhile, downstream applications with preprocessed data vary under different industrial scenes. The focus of this study is to develop a customized data imputation method for specific downstream applications such as soft sensing. A fine-tuned imputation GAN is designed with a soft sensor module so as to guide the data imputation for good imputation on key variables of the soft sensor. Considering that missing data exists not only in measurement variables but also in soft sensor labels, a semi-supervised soft sensor is designed to handle missing data in the labels, optimized together with the imputation model. The customized data imputation can thus improve the final performance of the downstream model which is a soft sensor in this work. The customization could be transferred to other applications such as an anomaly detection model as well. [ABSTRACT FROM AUTHOR]

In medical image analysis (MIA) and computer-assisted surgery (CAS), aligning two multiple point sets (PSs) together is an essential but also a challenging problem. For example, rigidly aligning multiple point sets into one common coordinate frame is a prerequisite for statistical shape modelling (SSM). Accurately aligning the pre-operative space with the intra-operative space in CAS is very crucial to successful interventions. In this article, we formally formulate the multiple generalized point set registration problem (MGPSR) in a probabilistic manner, where both the positional and the normal vectors are used. The six-dimensional vectors consisting of both positional and normal vectors are called as generalized points. In the formulated model, all the generalized PSs to be registered are considered to be the realizations of underlying unknown hybrid mixture models (HMMs). By assuming the independence of the positional and orientational vectors (i.e., the normal vectors), the probability density function (PDF) of an observed generalized point is computed as the product of Gaussian and Fisher distributions. Furthermore, to consider the anisotropic noise in surgical navigation, the positional error is assumed to obey a multi-variate Gaussian distribution. Finally, registering PSs is formulated as a maximum likelihood (ML) problem, and solved under the expectation maximization (EM) technique. By using more enriched information (i.e., the normal vectors), our algorithm is more robust to outliers. By treating all PSs equally, our algorithm does not bias towards any PS. To validate the proposed approach, extensive experiments have been conducted on surface points extracted from CT images of (i) a human femur bone model; (ii) a human pelvis bone model. Results demonstrate our algorithm’s high accuracy, robustness to noise and outliers. Note to Practitioners—This paper was motivated by solving the problem of registering two or more PSs. Most existing registration approaches use only the positional information associated with each point, and thus lacks robustness to noise and outliers. Three significant improvements are brought by our proposed approach. First, the normal vectors that can be extracted from the point sets are utilized in the registration. Second, the positional error distribution is assumed to be anisotropic and inhomogeneous. Third, all the PSs to be registered are treated equally that means no PS is considered as the model one. The registration problem is cast into a maximum likelihood (ML) problem and solved under the expectation maximization (EM) framework. We have demonstrated through extensive experiments that the proposed registration approach achieves significantly improved accuracy, robustness to noise and outliers. The algorithm is particularly suitable for biomedical applications involving the registration procedures, such as image-guided surgery. [ABSTRACT FROM AUTHOR]

Safe autonomous navigation is an essential and challenging problem for robots operating in highly unstructured or completely unknown environments. Under these conditions, not only robotic systems must deal with limited localization information but also their maneuverability is constrained by their dynamics and often suffers from uncertainty. In order to cope with these constraints, this article proposes an uncertainty-based framework for mapping and planning feasible motions online with probabilistic safety guarantees. The proposed approach deals with the motion, probabilistic safety, and online computation constraints by: 1) incrementally mapping the surroundings to build an uncertainty-aware representation of the environment and 2) iteratively (re)planning trajectories to goal that is kinodynamically feasible and probabilistically safe through a multilayered sampling-based planner in the belief space. In-depth empirical analyses illustrate some important properties of this approach, namely: 1) the multilayered planning strategy enables rapid exploration of the high-dimensional belief space while preserving asymptotic optimality and completeness guarantees and 2) the proposed routine for probabilistic collision checking results in tighter probability bounds in comparison to other uncertainty-aware planners in the literature. Furthermore, real-world in-water experimental evaluation on a nonholonomic torpedo-shaped autonomous underwater vehicle and simulated trials in an urban environment on an unmanned aerial vehicle demonstrate the efficacy of the method and its suitability for systems with limited onboard computational power. Note to Practitioners—Emergent robotic applications require operating in previously unmapped scenarios. This article presents a unified mapping–planning strategy that enables robots to navigate autonomously and safely in harsh environments. [ABSTRACT FROM AUTHOR]

Some response surface functions in complex engineering systems are usually highly nonlinear, unformed, and expensive to evaluate. To tackle this challenge, Bayesian optimization (BO), which conducts sequential design via a posterior distribution over the objective function, is a critical method used to find the global optimum of black-box functions. Kernel functions play an important role in shaping the posterior distribution of the estimated function. The widely used kernel function, e.g., radial basis function (RBF), is very vulnerable and susceptible to outliers; the existence of outliers is causing its Gaussian process (GP) surrogate model to be sporadic. In this article, we propose a robust kernel function, asymmetric elastic net radial basis function (AEN-RBF). Its validity as a kernel function and computational complexity are evaluated. When compared with the baseline RBF kernel, we prove theoretically that AEN-RBF can realize smaller mean squared prediction error under mild conditions. The proposed AEN-RBF kernel function can also realize faster convergence to the global optimum. We also show that the AEN-RBF kernel function is less sensitive to outliers, and hence improves the robustness of the corresponding BO with GPs. Through extensive evaluations carried out on synthetic and real-world optimization problems, we show that AEN-RBF outperforms the existing benchmark kernel functions. Note to Practitioners—Some industrial systems cannot be accurately represented by physical models. In this situation, data-driven black-box optimization is necessary for advancing the system automation and intelligence. BO is one of the widely used strategies for learning the global optimum of black-box functions. BO has been applied to robotics, anomaly detection, automatic learning algorithm configuration, reinforcement learning, and deep learning. This article proposes one new kernel function, named after AEN-RBF. The new kernel function will make BO with GPs more robust to outliers and lower the data quality barrier of model training. This article was motivated by the hyperparameter tuning problem of deep learning models for image defect detection in advanced manufacturing, but the method can be easily extended to other applications where kernel functions are needed. Our proposed method is verified by synthetic and real-world optimization problems. [ABSTRACT FROM AUTHOR]

Data centers are facilities with large number of servers providing cloud services. The increasing number of data centers in the last years has generated environmental concern due to the large amount of energy consumed by them. This also includes some auxiliary services such as the cooling equipment which is known to be very costly. For that reason, efficient data center strategies are needed in order to provide an acceptable quality of service (QoS) and suitable temperature for every server while using the least amount of resources possible. This article presents some strategies to deal with the unified workload and temperature problem that appears in the data center. As the system is modeled as a queue and the control variables have an hybrid nature, some highly parallelizable particle-based optimization algorithms are proposed to solve the optimization problem. Numerical simulations are provided in order to illustrate the effectiveness of the strategy. These simulations also show the improvements obtained from the GPU computing. Finally, a probabilistic evaluation approach is developed in order to provide certificates on the probability of constraint satisfaction without increasing the computational burden of the online problem. Note to Practitioners—This article addresses the problem of deciding in real-time the number of active servers in a data center that is required to meet the quality of service (QoS) demands while keeping energy consumption at a minimum. The temperature set point of the cooling equipment must also be taken into account, as it is advisable to use the minimum cooling that keeps the servers running in safe conditions. The management strategy proposed is based on predictive control. In this way, the number of active servers and temperature set point will be chosen so that the future energy consumption is minimized while guaranteeing that QoS and safety demands are met under different possible operating conditions. Furthermore, the proposed management strategy can be tuned depending on the QoS that it is desirable to provide. The proposed strategy will lead to energy-consumption improvements while having guarantees on the data center performance. [ABSTRACT FROM AUTHOR]

It is found from actual data that due to generation dispatch and uncertain renewable generations and loads with complicated correlations, inferring the probabilistic distributions for uncertain inputs is challenging. Many probabilistic power flow approaches have been developed in the literature but their validations using realistic systems and data are lacking. This paper proposes a data-driven probabilistic analysis approach for system risk assessment of the miniWECC system using actual data. The sparse Gaussian process (SGP) is advocated to quantify the impacts of uncertain inputs on voltage security. SGP does not need the probability distribution function of uncertain inputs, can handle correlations and is highly computationally efficient. Results on the miniWECC system using realistic data show that SGP outperforms existing approaches and is able to quantify the voltage violation risks. [ABSTRACT FROM AUTHOR]

Power system inertia is declining and is increasingly variable and uncertain in regions where the penetration of non-synchronous generation and interconnectors is growing. This presents a challenge to power system operators who must take appropriate actions to ensure the stability and security of power systems relying on short-term forecasts of the system’s inertial response. Existing models to forecast inertia fail to quantify uncertainty, which may prevent their utilization given the risk aversion of the system operators when handling stability issues. This paper is the first to develop a model to produce calibrated, data-driven probabilistic forecasts of the inertia contribution of transmission-connected synchronous generators. The model provides a necessary tool for system operators to quantify forecast uncertainty, allowing them to manage the risk of frequency instability cost-effectively. The paper demonstrates that the assumption of a Gaussian distribution of uncertainty applied in existing models is not acceptable to accurately forecast the inertial response and provides a satisfactory forecast model by combining non-parametric density forecasting with parametric tail distributions. Moreover, the paper shows that satisfactory predictive performance can only be achieved by adopting a rolling horizon forecast approach to deal with the rapidly changing characteristics of the inertial response in power systems. [ABSTRACT FROM AUTHOR]

We propose a chance-constrained formulation for the problem of dimensioning frequency restoration reserves on a power transmission network. We cast our problem as a two-stage stochastic mixed integer linear program, and propose a heuristic algorithm for solving the problem. Our model accounts for the simultaneous sizing of both upward and downward reserves, and uncertainty driven by imbalances, contingencies and available transmission capacity. Our core methodology is further adapted in order to minimize inter-zonal flows and in order to split reserve requirements between automatic and manual frequency restoration reserves. We apply our methodology to the problem of sizing reserves in the four load frequency control areas of the Swedish power system. We demonstrate the benefits of our method in terms of decreasing reserve requirements in the absence of reserve sharing, we analyze the spatial allocation of reserves, and we perform various sensitivity analyses. [ABSTRACT FROM AUTHOR]

Determining the quality of sensing devices exhibiting minimal digitization complexity is addressed. Measurements of such sensor systems are characterized by multivariate binary distributions and assessing sensitivity via the Cramér-Rao lower bound turns out to be intractable. In this context, the Fisher matrix of the exponential family and a lower bound for arbitrary probabilistic models are discussed. The conservative approximation for Fisher’s information matrix rests on a surrogate exponential family distribution connected to the actual data-generating system by two compact equivalences. Without characterizing the likelihood and its support, this probabilistic notion enables designing estimators that consistently achieve the sensitivity level defined by the inverse of the conservative information matrix. For hard-limited multivariate Gaussian signal models, a quadratic exponential surrogate distribution tames statistical complexity such that a quantitative and conservative assessment of Fisher information becomes possible. This result is exploited for the Fisherian quantization loss analysis of an array with low-complexity binary sensors in comparison to an ideal system featuring infinite amplitude resolution. Additionally, data-driven assessment by estimating a conservative approximation for the Fisher matrix under recursive binary sampling as implemented in ΣΔ-modulating analog-to-digital converters is demonstrated. [ABSTRACT FROM AUTHOR]

ChaCha has been one of the most prominent ARX designs of the last few years because of its use in several systems. The cryptanalysis of ChaCha involves a differential attack that exploits the idea of Probabilistic Neutral Bits (PNBs). For a long period, the single-bit distinguisher in this differential attack was found up to 3rd round. At Crypto 2020, Beierle et al. introduced for the first time the single bit distinguishers for 3.5th round, which contributed significantly to regaining the flow of the research work in this direction. This discovery became the primary factor behind the huge improvement in the key recovery attack complexity in that work. This was followed by another work at Eurocrypt 2021, where a single bit distinguisher at 3.5th round helped to produce a 7th round distinguisher of ChaCha and a further improvement in the key recovery. In this paper, first, we provide the theoretical framework for the distinguisher given by Beierle et al. We mathematically derive the observed differential correlation for the particular position where the output difference is observed at 3.5th round. Also, Beierle et al. mentioned the issue of the availability of proper IVs to produce such distinguishers, and pointed out that not all keys have such IVs available. Here we provide a theoretical insight of this issue. Next, we revisit the work of Coutinho et al. (Eurocrypt 2021). Using Differential-Linear attacks against ChaCha, they claimed the distinguisher and the key recovery with complexities 2218 and $2^{228.51}$ respectively. We show that the differential correlation for the 3.5th round is much smaller than the claim of Coutinho et al. This makes the attack complexities much higher than their claim. [ABSTRACT FROM AUTHOR]

There is a need to map underground pipelines due to nonavailable existing pipeline maps caused by poor management of statutory records and insufficient updating of documentation whenever pipeline construction or rerouting occurs. By fusing multisource data, a novel method to map underground pipelines is proposed in this article. Statutory records of the underground pipelines are converted into the initial pipeline map. Pipeline information obtained from manhole covers and remote sensing technologies are normalized into the pipeline dataset composed of detected points. The probabilistic pipeline mapping model (PPMM) is then proposed to map the buried pipelines from the conducted pipeline dataset, with or without statutory pipeline records. In this model, each detected point is classified into the specific pipeline that most likely generates the data of this point, and detected points generated from the same pipeline are fit to revise the pipelines’ locations and directions. The above classification and fitting operations are performed iteratively, and PPMM would output the pipeline map with the highest probability. Experimental studies on real-world datasets are conducted and analyzed, and the obtained results demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In many real situations, because of the lack or inaccuracy of data, it is difficult to evaluate the performance levels and state probabilities of multistate components with precise values. Thus, the reliability evaluation of systems is always affected by the epistemic uncertainty. Existing research on epistemic uncertainty just focuses on simple multistate systems, without considering the phased mission and performance sharing characteristics of systems. Besides, the impact of transmission loss and performance storage on reliability needs to be considered in the modeling of performance sharing systems. In this article, considering the epistemic uncertainty, transmission loss, and performance storage simultaneously, an efficient reliability evaluation method for multi-state phased mission systems with common bus performance sharing is proposed. The transmission loss during the processes thatperformance sharing between subsystems and transferring between phases is considered in the system model. A modified Markov model combined with the mass function is adopted to measure the precise belief degree of component states at any given moment. Then, the belief universal generating function (UGF) method based on the Dempster—Shafer evidence theory is utilized to evaluate the uncertainty of the system instantaneous availability. Finally, two case studies are carried out to demonstrate the effectiveness of the proposed method and explore the dynamic system availability under epistemic uncertainty. [ABSTRACT FROM AUTHOR]

The striking growth of powerful computing resources allows time-efficient solution of computationally demanding problems. In particular, advances in high-performance computing have made stochastic approaches to real-world applications more practical. The belief propagation (BP) algorithm is a probabilistic method typically used in information theory and artificial intelligence. This article exploits the probabilistic message passing attribute of BP for solving stochastic linear systems that naturally arise from finite element formulation of stochastic partial differential equations (PDEs), establishing an explicit connection between the two fields for the first time. The accuracy of the algorithm is validated by comparison to the well-known Monte Carlo method. [ABSTRACT FROM AUTHOR]

A novel probabilistic sparsity-promoting method for robust near-field (NF) antenna characterization is proposed. It leverages on the measurements-by-design (MebD) paradigm, and it exploits some a priori information on the antenna under test (AUT) to generate an overcomplete representation basis. Accordingly, the problem at hand is reformulated in a compressive sensing (CS) framework as the retrieval of a maximally sparse distribution (with respect to the overcomplete basis) from a reduced set of measured data, and then, it is solved by means of a Bayesian strategy. Representative numerical results are presented to, also comparatively, assess the effectiveness of the proposed approach in reducing the “burden/cost” of the acquisition process and mitigate (possible) truncation errors when dealing with space-constrained probing systems. [ABSTRACT FROM AUTHOR]

This article focuses on target search in dynamic environments using multiple solar-powered unmanned aerial vehicles (SUAVs) with the probability map method. First, the energy model of the SUAV and an external solar environment model are established. Second, the Gaussian mixture model (GMM) is used to extract the prior probability distribution of the target to obtain multiple search areas composed of two-dimensional Gaussian distributions. Then, dynamic task allocation of the SUAVs based on the environment is performed utilizing the GMM information. Next, the SUAVs search for the target according to the assignment and plan a path with the energy model and probability established before, and the probability map is updated in real time according to the detection result of the SUAVs and the velocity vector field of the environment. In this study, two probability map update methods, namely the equivalent area iteration (EAI) and probability estimated diffusion (PED) methods, are proposed for the situations of precise and imprecise environmental information, respectively. Finally, comparative simulations are carried out for these two different situations to prove the improvement obtained using SUAVs. [ABSTRACT FROM AUTHOR]

In a real life process evolving over time, the relationship between its relevant variables may change. Therefore, it is advantageous to have different inference models for each state of the process. Asymmetric hidden Markov models fulfil this dynamical requirement and provide a framework where the trend of the process can be expressed as a latent variable. In this paper, we modify these recent asymmetric hidden Markov models to have an asymmetric autoregressive component in the case of continuous variables, allowing the model to choose the order of autoregression that maximizes its penalized likelihood for a given training set. Additionally, we show how inference, hidden states decoding and parameter learning must be adapted to fit the proposed model. Finally, we run experiments with synthetic and real data to show the capabilities of this new model. [ABSTRACT FROM AUTHOR]

Large-scale and multidimensional spatiotemporal data sets are becoming ubiquitous in many real-world applications such as monitoring urban traffic and air quality. Making predictions on these time series has become a critical challenge due to not only the large-scale and high-dimensional nature but also the considerable amount of missing data. In this paper, we propose a Bayesian temporal factorization (BTF) framework for modeling multidimensional time series—in particular spatiotemporal data—in the presence of missing values. By integrating low-rank matrix/tensor factorization and vector autoregressive (VAR) process into a single probabilistic graphical model, this framework can characterize both global and local consistencies in large-scale time series data. The graphical model allows us to effectively perform probabilistic predictions and produce uncertainty estimates without imputing those missing values. We develop efficient Gibbs sampling algorithms for model inference and model updating for real-time prediction and test the proposed BTF framework on several real-world spatiotemporal data sets for both missing data imputation and multi-step rolling prediction tasks. The numerical experiments demonstrate the superiority of the proposed BTF approaches over existing state-of-the-art methods. [ABSTRACT FROM AUTHOR]

The Dempster–Shafer (D-S) evidence theory has been widely used in many fields from probabilistic inference, information fusion to decision analysis due to its superiority to formulate uncertain and incomplete information under a weaker condition than the Bayesian probability theory. To support the elicitation of basic probability assignment (BPA), numerous uncertainty measures have been proposed in the recent decades, which take into account nonspecificity and structural conflict (SC) in either the entropy-alike or nonentropy form. This article is focused primarily on developing a generalized belief entropy to measure and quantify the uncertainty of BPA in a consistent and comprehensive way. The definition of the proposed belief entropy involves three components. Specifically, the first component is Shannon’s definition of entropy of probability functions which can be interpreted as the measure of discord of the mass function among various focal elements. The second component is the measure of total nonspecificity which is the generalization of Dubois–Prade’s definition of nonspecificity measure. Furthermore, the critical component introduced in this article is the utilization of the SC coefficient within an evidence, which fully considers the intersection between each pair of focal elements of the BPA. The characteristics and properties of the new generalized belief entropy are analyzed systematically with theoretical proofs. Finally, the proposed belief entropy is embedded to a three-tuple approach to deal with a practical multiple attribute decision-making (MADM) problem to demonstrate its validity and strengths of measuring nonspecificity and SC in uncertain decision making. [ABSTRACT FROM AUTHOR]

We study the problem of simultaneous search for multiple targets over a multidimensional unit cube and derive fundamental resolution limits of non-adaptive querying procedures using the 20 questions estimation framework. The performance criterion that we consider is the achievable resolution, which is defined as the maximal $L_\infty $ norm between the location vector and its estimated version where the maximization is over all target location vectors. The fundamental resolution limit is defined as the minimal achievable resolution of any non-adaptive query procedure, where each query has binary yes/no answers. We drive non-asymptotic and second-order asymptotic bounds on the minimal achievable resolution, using tools from finite blocklength information theory. Specifically, in the achievability part, we relate the 20 questions problem to data transmission over a multiple access channel, use the information spectrum method by Han and borrow results from finite blocklength analysis for random access channel coding. In the converse part, we relate the 20 questions problem to data transmission over a point-to-point channel and adapt finite blocklength converse results for channel coding. Our results extend the purely first-order asymptotic analyses of Kaspi et al. (ISIT 2015) for the one-dimensional case: we consider channels beyond the binary symmetric channel and derive non-asymptotic and second-order asymptotic bounds on the performance of optimal non-adaptive query procedures. [ABSTRACT FROM AUTHOR]

We extend the classical problem of privacy amplification to a setting where the active adversary, Eve, is also allowed to fully corrupt the internal memory (which includes the shared randomness, and local randomness tape) of one of the honest parties, Alice and Bob, before the execution of the protocol. We require that either one of Alice or Bob detects tampering, or they agree on a shared key that is indistinguishable from the uniform distribution to Eve. We obtain the following results: 1) we give a privacy amplification protocol via low-error non-malleable two-source extractors with one source having low min-entropy. In particular, this implies the existence of such (non-efficient) protocols; 2) we show that even slight improvements to the state-of-the-art explicit non-malleable two-source extractors would lead to explicit low-error, low min-entropy two-source extractors, thereby resolving a long-standing open question. This suggests that obtaining (information-theoretically secure) explicit non-malleable two-source extractors for (1) might be hard; 3) we present explicit constructions of low-error, low min-entropy non-malleable two-source extractors in the CRS model of (Garg, Kalai, Khurana, Eurocrypt 2020), assuming either the quasi-polynomial hardness of DDH or the existence of nearly-optimal collision-resistant hash functions; 4) we instantiate our privacy amplification protocol with the above mentioned non-malleable two-source extractors in the CRS model, leading to explicit, computationally-secure protocols. This is not immediate from (1) because in the computational setting we need to make sure that, in particular, all randomness sources remain samplable throughout the proof. This requires upgrading the assumption of quasi-polynomial hardness of DDH to sub-exponential hardness of DDH.We emphasize that each of the first three results can be read independently. [ABSTRACT FROM AUTHOR]