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We study the approximation capacity of deep ReLU recurrent neural networks (RNNs) and explore the convergence properties of nonparametric least squares regression using RNNs. We derive upper bounds on the approximation error of RNNs for H\"older smooth functions, in the sense that the output at each time step of an RNN can approximate a H\"older function that depends only on past and current information, termed a past-dependent function. This allows a carefully constructed RNN to simultaneously approximate a sequence of past-dependent H\"older functions. We apply these approximation results to derive non-asymptotic upper bounds for the prediction error of the empirical risk minimizer in regression problem. Our error bounds achieve minimax optimal rate under both exponentially $\beta$-mixing and i.i.d. data assumptions, improving upon existing ones. Our results provide statistical guarantees on the performance of RNNs.

Machine learning is a rapidly advancing field with diverse applications across various domains. One prominent area of research is the utilization of deep learning techniques for solving partial differential equations(PDEs). In this work, we specifically focus on employing a three-layer tanh neural network within the framework of the deep Ritz method(DRM) to solve second-order elliptic equations with three different types of boundary conditions. We perform projected gradient descent(PDG) to train the three-layer network and we establish its global convergence. To the best of our knowledge, we are the first to provide a comprehensive error analysis of using overparameterized networks to solve PDE problems, as our analysis simultaneously includes estimates for approximation error, generalization error, and optimization error. We present error bound in terms of the sample size $n$ and our work provides guidance on how to set the network depth, width, step size, and number of iterations for the projected gradient descent algorithm. Importantly, our assumptions in this work are classical and we do not require any additional assumptions on the solution of the equation. This ensures the broad applicability and generality of our results.

We present theoretical convergence guarantees for ODE-based generative models, specifically flow matching. We use a pre-trained autoencoder network to map high-dimensional original inputs to a low-dimensional latent space, where a transformer network is trained to predict the velocity field of the transformation from a standard normal distribution to the target latent distribution. Our error analysis demonstrates the effectiveness of this approach, showing that the distribution of samples generated via estimated ODE flow converges to the target distribution in the Wasserstein-2 distance under mild and practical assumptions. Furthermore, we show that arbitrary smooth functions can be effectively approximated by transformer networks with Lipschitz continuity, which may be of independent interest.

Data scarcity hinders the usability of data-dependent algorithms when tackling IoT intrusion detection (IID). To address this, we utilise the data rich network intrusion detection (NID) domain to facilitate more accurate intrusion detection for IID domains. In this paper, a Geometric Graph Alignment (GGA) approach is leveraged to mask the geometric heterogeneities between domains for better intrusion knowledge transfer. Specifically, each intrusion domain is formulated as a graph where vertices and edges represent intrusion categories and category-wise interrelationships, respectively. The overall shape is preserved via a confused discriminator incapable to identify adjacency matrices between different intrusion domain graphs. A rotation avoidance mechanism and a centre point matching mechanism is used to avoid graph misalignment due to rotation and symmetry, respectively. Besides, category-wise semantic knowledge is transferred to act as vertex-level alignment. To exploit the target data, a pseudo-label election mechanism that jointly considers network prediction, geometric property and neighbourhood information is used to produce fine-grained pseudo-label assignment. Upon aligning the intrusion graphs geometrically from different granularities, the transferred intrusion knowledge can boost IID performance. Comprehensive experiments on several intrusion datasets demonstrate state-of-the-art performance of the GGA approach and validate the usefulness of GGA constituting components., Comment: Accepted by IEEE Internet of Things Journal

We study the stochastic contextual bandit with knapsacks (CBwK) problem, where each action, taken upon a context, not only leads to a random reward but also costs a random resource consumption in a vector form. The challenge is to maximize the total reward without violating the budget for each resource. We study this problem under a general realizability setting where the expected reward and expected cost are functions of contexts and actions in some given general function classes $\mathcal{F}$ and $\mathcal{G}$, respectively. Existing works on CBwK are restricted to the linear function class since they use UCB-type algorithms, which heavily rely on the linear form and thus are difficult to extend to general function classes. Motivated by online regression oracles that have been successfully applied to contextual bandits, we propose the first universal and optimal algorithmic framework for CBwK by reducing it to online regression. We also establish the lower regret bound to show the optimality of our algorithm for a variety of function classes., Comment: AISTATS2023

Time series underwent the transition from statistics to deep learning, as did many other machine learning fields. Although it appears that the accuracy has been increasing as the model is updated in a number of publicly available datasets, it typically only increases the scale by several times in exchange for a slight difference in accuracy. Through this experiment, we point out a different line of thinking, time series, especially long-term forecasting, may differ from other fields. It is not necessary to use extensive and complex models to grasp all aspects of time series, but to use pure models to grasp the core rules of time series changes. With this simple but effective idea, we created PureTS, a network with three pure linear layers that achieved state-of-the-art in 80% of the long sequence prediction tasks while being nearly the lightest model and having the fastest running speed. On this basis, we discuss the potential of pure linear layers in both phenomena and essence. The ability to understand the core law contributes to the high precision of long-distance prediction, and reasonable fluctuation prevents it from distorting the curve in multi-step prediction like mainstream deep learning models, which is summarized as a pure linear neural network that avoids over-fluctuating. Finally, we suggest the fundamental design standards for lightweight long-step time series tasks: input and output should try to have the same dimension, and the structure avoids fragmentation and complex operations., Comment: To be submitted to the conference

Differentially private (DP) stochastic convex optimization (SCO) is ubiquitous in trustworthy machine learning algorithm design. This paper studies the DP-SCO problem with streaming data sampled from a distribution and arrives sequentially. We also consider the continual release model where parameters related to private information are updated and released upon each new data, often known as the online algorithms. Despite that numerous algorithms have been developed to achieve the optimal excess risks in different $\ell_p$ norm geometries, yet none of the existing ones can be adapted to the streaming and continual release setting. To address such a challenge as the online convex optimization with privacy protection, we propose a private variant of online Frank-Wolfe algorithm with recursive gradients for variance reduction to update and reveal the parameters upon each data. Combined with the adaptive differential privacy analysis, our online algorithm achieves in linear time the optimal excess risk when $1

This paper studies the approximation capacity of ReLU neural networks with norm constraint on the weights. We prove upper and lower bounds on the approximation error of these networks for smooth function classes. The lower bound is derived through the Rademacher complexity of neural networks, which may be of independent interest. We apply these approximation bounds to analyze the convergences of regression using norm constrained neural networks and distribution estimation by GANs. In particular, we obtain convergence rates for over-parameterized neural networks. It is also shown that GANs can achieve optimal rate of learning probability distributions, when the discriminator is a properly chosen norm constrained neural network.

We derive nearly sharp bounds for the bidirectional GAN (BiGAN) estimation error under the Dudley distance between the latent joint distribution and the data joint distribution with appropriately specified architecture of the neural networks used in the model. To the best of our knowledge, this is the first theoretical guarantee for the bidirectional GAN learning approach. An appealing feature of our results is that they do not assume the reference and the data distributions to have the same dimensions or these distributions to have bounded support. These assumptions are commonly assumed in the existing convergence analysis of the unidirectional GANs but may not be satisfied in practice. Our results are also applicable to the Wasserstein bidirectional GAN if the target distribution is assumed to have a bounded support. To prove these results, we construct neural network functions that push forward an empirical distribution to another arbitrary empirical distribution on a possibly different-dimensional space. We also develop a novel decomposition of the integral probability metric for the error analysis of bidirectional GANs. These basic theoretical results are of independent interest and can be applied to other related learning problems., Comment: Corresponding authors: Yunfei Yang (yyangdc@connect.ust.hk), Jian Huang (jian-huang@uiowa.edu), Yuling Jiao (yulingjiaomath@whu.edu.cn)

Contextual bandit algorithms are useful in personalized online decision-making. However, many applications such as personalized medicine and online advertising require the utilization of individual-specific information for effective learning, while user's data should remain private from the server due to privacy concerns. This motivates the introduction of local differential privacy (LDP), a stringent notion in privacy, to contextual bandits. In this paper, we design LDP algorithms for stochastic generalized linear bandits to achieve the same regret bound as in non-privacy settings. Our main idea is to develop a stochastic gradient-based estimator and update mechanism to ensure LDP. We then exploit the flexibility of stochastic gradient descent (SGD), whose theoretical guarantee for bandit problems is rarely explored, in dealing with generalized linear bandits. We also develop an estimator and update mechanism based on Ordinary Least Square (OLS) for linear bandits. Finally, we conduct experiments with both simulation and real-world datasets to demonstrate the consistently superb performance of our algorithms under LDP constraints with reasonably small parameters $(\varepsilon, \delta)$ to ensure strong privacy protection.

This paper studies how well generative adversarial networks (GANs) learn probability distributions from finite samples. Our main results establish the convergence rates of GANs under a collection of integral probability metrics defined through H\"older classes, including the Wasserstein distance as a special case. We also show that GANs are able to adaptively learn data distributions with low-dimensional structures or have H\"older densities, when the network architectures are chosen properly. In particular, for distributions concentrated around a low-dimensional set, we show that the learning rates of GANs do not depend on the high ambient dimension, but on the lower intrinsic dimension. Our analysis is based on a new oracle inequality decomposing the estimation error into the generator and discriminator approximation error and the statistical error, which may be of independent interest.

Missing node attributes is a common problem in real-world graphs. Graph neural networks have been demonstrated power in graph representation learning while their performance is affected by the completeness of graph information. Most of them are not specified for missing-attribute graphs and fail to leverage incomplete attribute information effectively. In this paper, we propose an innovative node representation learning framework, Wasserstein Graph Neural Network (WGNN), to mitigate the problem. To make the most of limited observed attribute information and capture the uncertainty caused by missing values, we express nodes as low-dimensional distributions derived from the decomposition of the attribute matrix. Furthermore, we strengthen the expressiveness of representations by developing a novel message passing schema that aggregates distributional information from neighbors in the Wasserstein space. We test WGNN in node classification tasks under two missing-attribute cases on both synthetic and real-world datasets. In addition, we find WGNN suitable to recover missing values and adapt them to tackle matrix completion problems with graphs of users and items. Experimental results on both tasks demonstrate the superiority of our method.

We study the efficacy and efficiency of deep generative networks for approximating probability distributions. We prove that neural networks can transform a low-dimensional source distribution to a distribution that is arbitrarily close to a high-dimensional target distribution, when the closeness are measured by Wasserstein distances and maximum mean discrepancy. Upper bounds of the approximation error are obtained in terms of the width and depth of neural network. Furthermore, it is shown that the approximation error in Wasserstein distance grows at most linearly on the ambient dimension and that the approximation order only depends on the intrinsic dimension of the target distribution. On the contrary, when $f$-divergences are used as metrics of distributions, the approximation property is different. We show that in order to approximate the target distribution in $f$-divergences, the dimension of the source distribution cannot be smaller than the intrinsic dimension of the target distribution.

Nonnegative matrix factorization is usually powerful for learning the "shallow" parts-based representation, but it clearly fails to discover deep hierarchical information within both the basis and representation spaces. In this paper, we technically propose a new enriched prior based Dual-constrained Deep Semi-Supervised Coupled Factorization Network, called DS2CF-Net, for learning the hierarchical coupled representations. To ex-tract hidden deep features, DS2CF-Net is modeled as a deep-structure and geometrical structure-constrained neural network. Specifically, DS2CF-Net designs a deep coupled factorization architecture using multi-layers of linear transformations, which coupled updates the bases and new representations in each layer. To improve the discriminating ability of learned deep representations and deep coefficients, our network clearly considers enriching the supervised prior by the joint deep coefficients-regularized label prediction, and incorporates enriched prior information as additional label and structure constraints. The label constraint can enable the samples of the same label to have the same coordinate in the new feature space, while the structure constraint forces the coefficient matrices in each layer to be block-diagonal so that the enhanced prior using the self-expressive label propagation are more accurate. Our network also integrates the adaptive dual-graph learning to retain the local manifold structures of both the data manifold and feature manifold by minimizing the reconstruction errors in each layer. Extensive experiments on several real databases demonstrate that our DS2CF-Net can obtain state-of-the-art performance for representation learning and clustering., Comment: International Journal of Computer Vision (IJCV), Sep 2021

Generative Adversarial Nets (GAN) have received considerable attention since the 2014 groundbreaking work by Goodfellow et al. Such attention has led to an explosion in new ideas, techniques and applications of GANs. To better understand GANs we need to understand the mathematical foundation behind them. This paper attempts to provide an overview of GANs from a mathematical point of view. Many students in mathematics may find the papers on GANs more difficulty to fully understand because most of them are written from computer science and engineer point of view. The aim of this paper is to give more mathematically oriented students an introduction to GANs in a language that is more familiar to them.

Partial Multi-label Learning (PML) aims to induce the multi-label predictor from datasets with noisy supervision, where each training instance is associated with several candidate labels but only partially valid. To address the noisy issue, the existing PML methods basically recover the ground-truth labels by leveraging the ground-truth confidence of the candidate label, \ie the likelihood of a candidate label being a ground-truth one. However, they neglect the information from non-candidate labels, which potentially contributes to the ground-truth label recovery. In this paper, we propose to recover the ground-truth labels, \ie estimating the ground-truth confidences, from the label enrichment, composed of the relevance degrees of candidate labels and irrelevance degrees of non-candidate labels. Upon this observation, we further develop a novel two-stage PML method, namely \emph{\underline{P}artial \underline{M}ulti-\underline{L}abel \underline{L}earning with \underline{L}abel \underline{E}nrichment-\underline{R}ecovery} (\baby), where in the first stage, it estimates the label enrichment with unconstrained label propagation, then jointly learns the ground-truth confidence and multi-label predictor given the label enrichment. Experimental results validate that \baby outperforms the state-of-the-art PML methods., Comment: Appeared at IJCAI 2020

We study the expressive power of deep ReLU neural networks for approximating functions in dilated shift-invariant spaces, which are widely used in signal processing, image processing, communications and so on. Approximation error bounds are estimated with respect to the width and depth of neural networks. The network construction is based on the bit extraction and data-fitting capacity of deep neural networks. As applications of our main results, the approximation rates of classical function spaces such as Sobolev spaces and Besov spaces are obtained. We also give lower bounds of the $L^p (1\le p \le \infty)$ approximation error for Sobolev spaces, which show that our construction of neural network is asymptotically optimal up to a logarithmic factor.

We propose a simple yet effective multiple kernel clustering algorithm, termed simple multiple kernel k-means (SimpleMKKM). It extends the widely used supervised kernel alignment criterion to multi-kernel clustering. Our criterion is given by an intractable minimization-maximization problem in the kernel coefficient and clustering partition matrix. To optimize it, we re-formulate the problem as a smooth minimization one, which can be solved efficiently using a reduced gradient descent algorithm. We theoretically analyze the performance of SimpleMKKM in terms of its clustering generalization error. Comprehensive experiments on 11 benchmark datasets demonstrate that SimpleMKKM outperforms state of the art multi-kernel clustering alternatives.

In this paper, we investigate the robust dictionary learning (DL) to discover the hybrid salient low-rank and sparse representation in a factorized compressed space. A Joint Robust Factorization and Projective Dictionary Learning (J-RFDL) model is presented. The setting of J-RFDL aims at improving the data representations by enhancing the robustness to outliers and noise in data, encoding the reconstruction error more accurately and obtaining hybrid salient coefficients with accurate reconstruction ability. Specifically, J-RFDL performs the robust representation by DL in a factorized compressed space to eliminate the negative effects of noise and outliers on the results, which can also make the DL process efficient. To make the encoding process robust to noise in data, J-RFDL clearly uses sparse L2, 1-norm that can potentially minimize the factorization and reconstruction errors jointly by forcing rows of the reconstruction errors to be zeros. To deliver salient coefficients with good structures to reconstruct given data well, J-RFDL imposes the joint low-rank and sparse constraints on the embedded coefficients with a synthesis dictionary. Based on the hybrid salient coefficients, we also extend J-RFDL for the joint classification and propose a discriminative J-RFDL model, which can improve the discriminating abilities of learnt coeffi-cients by minimizing the classification error jointly. Extensive experiments on public datasets demonstrate that our formulations can deliver superior performance over other state-of-the-art methods., Comment: Accepted by IEEE TIP

Both the Dictionary Learning (DL) and Convolutional Neural Networks (CNN) are powerful image representation learning systems based on different mechanisms and principles, however whether we can seamlessly integrate them to improve the per-formance is noteworthy exploring. To address this issue, we propose a novel generalized end-to-end representation learning architecture, dubbed Convolutional Dictionary Pair Learning Network (CDPL-Net) in this paper, which integrates the learning schemes of the CNN and dictionary pair learning into a unified framework. Generally, the architecture of CDPL-Net includes two convolutional/pooling layers and two dictionary pair learn-ing (DPL) layers in the representation learning module. Besides, it uses two fully-connected layers as the multi-layer perception layer in the nonlinear classification module. In particular, the DPL layer can jointly formulate the discriminative synthesis and analysis representations driven by minimizing the batch based reconstruction error over the flatted feature maps from the convolution/pooling layer. Moreover, DPL layer uses l1-norm on the analysis dictionary so that sparse representation can be delivered, and the embedding process will also be robust to noise. To speed up the training process of DPL layer, the efficient stochastic gradient descent is used. Extensive simulations on real databases show that our CDPL-Net can deliver enhanced performance over other state-of-the-art methods., Comment: Accepted by the 24th European Conference on Artificial Intelligence (ECAI 2020)

In this paper we propose to solve an important problem in recommendation -- user cold start, based on meta leaning method. Previous meta learning approaches finetune all parameters for each new user, which is both computing and storage expensive. In contrast, we divide model parameters into fixed and adaptive parts and develop a two-stage meta learning algorithm to learn them separately. The fixed part, capturing user invariant features, is shared by all users and is learned during offline meta learning stage. The adaptive part, capturing user specific features, is learned during online meta learning stage. By decoupling user invariant parameters from user dependent parameters, the proposed approach is more efficient and storage cheaper than previous methods. It also has potential to deal with catastrophic forgetting while continually adapting for streaming coming users. Experiments on production data demonstrates that the proposed method converges faster and to a better performance than baseline methods. Meta-training without online meta model finetuning increases the AUC from 72.24% to 74.72% (2.48% absolute improvement). Online meta training achieves a further gain of 2.46\% absolute improvement comparing with offline meta training.

In this paper, we consider the sigmoid Gaussian Hawkes process model: the baseline intensity and triggering kernel of Hawkes process are both modeled as the sigmoid transformation of random trajectories drawn from Gaussian processes (GP). By introducing auxiliary latent random variables (branching structure, P\'{o}lya-Gamma random variables and latent marked Poisson processes), the likelihood is converted to two decoupled components with a Gaussian form which allows for an efficient conjugate analytical inference. Using the augmented likelihood, we derive an expectation-maximization (EM) algorithm to obtain the maximum a posteriori (MAP) estimate. Furthermore, we extend the EM algorithm to an efficient approximate Bayesian inference algorithm: mean-field variational inference. We demonstrate the performance of two algorithms on simulated fictitious data. Experiments on real data show that our proposed inference algorithms can recover well the underlying prompting characteristics efficiently.

We investigate the sample size requirement for exact recovery of a high order tensor of low rank from a subset of its entries. In the Tucker decomposition framework, we show that the Riemannian optimization algorithm with initial value obtained from a spectral method can reconstruct a tensor of size $n\times n \times\cdots \times n$ tensor of ranks $(r,\cdots,r)$ with high probability from as few as $O((r^d+dnr)\log(d))$ entries. In the case of order 3 tensor, the entries can be asymptotically as few as $O(nr)$ for a low rank large tensor. We show the theoretical guarantee condition for the recovery. The analysis relies on the tensor restricted isometry property (tensor RIP) and the curvature of the low rank tensor manifold. Our algorithm is computationally efficient and easy to implement. Numerical results verify that the algorithms are able to recover a low rank tensor from minimum number of measurements. The experiments on hyperspectral images recovery also show that our algorithm is capable of real world signal processing problems., Comment: There is an error in the paper and need to be correct

In classical Hawkes process, the baseline intensity and triggering kernel are assumed to be a constant and parametric function respectively, which limits the model flexibility. To generalize it, we present a fully Bayesian nonparametric model, namely Gaussian process modulated Hawkes process and propose an EM-variational inference scheme. In this model, a transformation of Gaussian process is used as a prior on the baseline intensity and triggering kernel. By introducing a latent branching structure, the inference of baseline intensity and triggering kernel is decoupled and the variational inference scheme is embedded into an EM framework naturally. We also provide a series of schemes to accelerate the inference. Results of synthetic and real data experiments show that the underlying baseline intensity and triggering kernel can be recovered without parametric restriction and our Bayesian nonparametric estimation is superior to other state of the arts.

To address the challenges in learning deep generative models (e.g.,the blurriness of variational auto-encoder and the instability of training generative adversarial networks, we propose a novel deep generative model, named Wasserstein-Wasserstein auto-encoders (WWAE). We formulate WWAE as minimization of the penalized optimal transport between the target distribution and the generated distribution. By noticing that both the prior $P_Z$ and the aggregated posterior $Q_Z$ of the latent code Z can be well captured by Gaussians, the proposed WWAE utilizes the closed-form of the squared Wasserstein-2 distance for two Gaussians in the optimization process. As a result, WWAE does not suffer from the sampling burden and it is computationally efficient by leveraging the reparameterization trick. Numerical results evaluated on multiple benchmark datasets including MNIST, fashion- MNIST and CelebA show that WWAE learns better latent structures than VAEs and generates samples of better visual quality and higher FID scores than VAEs and GANs.

We propose a general framework to learn deep generative models via \textbf{V}ariational \textbf{Gr}adient Fl\textbf{ow} (VGrow) on probability spaces. The evolving distribution that asymptotically converges to the target distribution is governed by a vector field, which is the negative gradient of the first variation of the $f$-divergence between them. We prove that the evolving distribution coincides with the pushforward distribution through the infinitesimal time composition of residual maps that are perturbations of the identity map along the vector field. The vector field depends on the density ratio of the pushforward distribution and the target distribution, which can be consistently learned from a binary classification problem. Connections of our proposed VGrow method with other popular methods, such as VAE, GAN and flow-based methods, have been established in this framework, gaining new insights of deep generative learning. We also evaluated several commonly used divergences, including Kullback-Leibler, Jensen-Shannon, Jeffrey divergences as well as our newly discovered `logD' divergence which serves as the objective function of the logD-trick GAN. Experimental results on benchmark datasets demonstrate that VGrow can generate high-fidelity images in a stable and efficient manner, achieving competitive performance with state-of-the-art GANs.

Interpretation and diagnosis of machine learning models have gained renewed interest in recent years with breakthroughs in new approaches. We present Manifold, a framework that utilizes visual analysis techniques to support interpretation, debugging, and comparison of machine learning models in a more transparent and interactive manner. Conventional techniques usually focus on visualizing the internal logic of a specific model type (i.e., deep neural networks), lacking the ability to extend to a more complex scenario where different model types are integrated. To this end, Manifold is designed as a generic framework that does not rely on or access the internal logic of the model and solely observes the input (i.e., instances or features) and the output (i.e., the predicted result and probability distribution). We describe the workflow of Manifold as an iterative process consisting of three major phases that are commonly involved in the model development and diagnosis process: inspection (hypothesis), explanation (reasoning), and refinement (verification). The visual components supporting these tasks include a scatterplot-based visual summary that overviews the models' outcome and a customizable tabular view that reveals feature discrimination. We demonstrate current applications of the framework on the classification and regression tasks and discuss other potential machine learning use scenarios where Manifold can be applied.

This short paper describes our solution to the 2018 IEEE World Congress on Computational Intelligence One-Minute Gradual-Emotional Behavior Challenge, whose goal was to estimate continuous arousal and valence values from short videos. We designed four base regression models using visual and audio features, and then used a spectral approach to fuse them to obtain improved performance.

Predicting fine-grained interests of users with temporal behavior is important to personalization and information filtering applications. However, existing interest prediction methods are incapable of capturing the subtle degreed user interests towards particular items, and the internal time-varying drifting attention of individuals is not studied yet. Moreover, the prediction process can also be affected by inter-personal influence, known as behavioral mutual infectivity. Inspired by point process in modeling temporal point process, in this paper we present a deep prediction method based on two recurrent neural networks (RNNs) to jointly model each user's continuous browsing history and asynchronous event sequences in the context of inter-user behavioral mutual infectivity. Our model is able to predict the fine-grained interest from a user regarding a particular item and corresponding timestamps when an occurrence of event takes place. The proposed approach is more flexible to capture the dynamic characteristic of event sequences by using the temporal point process to model event data and timely update its intensity function by RNNs. Furthermore, to improve the interpretability of the model, the attention mechanism is introduced to emphasize both intra-personal and inter-personal behavior influence over time. Experiments on real datasets demonstrate that our model outperforms the state-of-the-art methods in fine-grained user interest prediction., Comment: Several existing references are missing and not discussed explicitly

This paper presents two unsupervised learning layers (UL layers) for label-free video analysis: one for fully connected layers, and the other for convolutional ones. The proposed UL layers can play two roles: they can be the cost function layer for providing global training signal; meanwhile they can be added to any regular neural network layers for providing local training signals and combined with the training signals backpropagated from upper layers for extracting both slow and fast changing features at layers of different depths. Therefore, the UL layers can be used in either pure unsupervised or semi-supervised settings. Both a closed-form solution and an online learning algorithm for two UL layers are provided. Experiments with unlabeled synthetic and real-world videos demonstrated that the neural networks equipped with UL layers and trained with the proposed online learning algorithm can extract shape and motion information from video sequences of moving objects. The experiments demonstrated the potential applications of UL layers and online learning algorithm to head orientation estimation and moving object localization.

Safeguarding privacy in machine learning is highly desirable, especially in collaborative studies across many organizations. Privacy-preserving distributed machine learning (based on cryptography) is popular to solve the problem. However, existing cryptographic protocols still incur excess computational overhead. Here, we make a novel observation that this is partially due to naive adoption of mainstream numerical optimization (e.g., Newton method) and failing to tailor for secure computing. This work presents a contrasting perspective: customizing numerical optimization specifically for secure settings. We propose a seemingly less-favorable optimization method that can in fact significantly accelerate privacy-preserving logistic regression. Leveraging this new method, we propose two new secure protocols for conducting logistic regression in a privacy-preserving and distributed manner. Extensive theoretical and empirical evaluations prove the competitive performance of our two secure proposals while without compromising accuracy or privacy: with speedup up to 2.3x and 8.1x, respectively, over state-of-the-art; and even faster as data scales up. Such drastic speedup is on top of and in addition to performance improvements from existing (and future) state-of-the-art cryptography. Our work provides a new way towards efficient and practical privacy-preserving logistic regression for large-scale studies which are common for modern science., Comment: 24 pages, 4 figures. Work done and circulated since 2015

Multi-view spectral clustering, which aims at yielding an agreement or consensus data objects grouping across multi-views with their graph laplacian matrices, is a fundamental clustering problem. Among the existing methods, Low-Rank Representation (LRR) based method is quite superior in terms of its effectiveness, intuitiveness and robustness to noise corruptions. However, it aggressively tries to learn a common low-dimensional subspace for multi-view data, while inattentively ignoring the local manifold structure in each view, which is critically important to the spectral clustering; worse still, the low-rank minimization is enforced to achieve the data correlation consensus among all views, failing to flexibly preserve the local manifold structure for each view. In this paper, 1) we propose a multi-graph laplacian regularized LRR with each graph laplacian corresponding to one view to characterize its local manifold structure. 2) Instead of directly enforcing the low-rank minimization among all views for correlation consensus, we separately impose low-rank constraint on each view, coupled with a mutual structural consensus constraint, where it is able to not only well preserve the local manifold structure but also serve as a constraint for that from other views, which iteratively makes the views more agreeable. Extensive experiments on real-world multi-view data sets demonstrate its superiority., Comment: Accepted to appear in IJCAI 2016

Stochastic partition models tailor a product space into a number of rectangular regions such that the data within each region exhibit certain types of homogeneity. Due to constraints of partition strategy, existing models may cause unnecessary dissections in sparse regions when fitting data in dense regions. To alleviate this limitation, we propose a parsimonious partition model, named Stochastic Patching Process (SPP), to deal with multi-dimensional arrays. SPP adopts an "enclosing" strategy to attach rectangular patches to dense regions. SPP is self-consistent such that it can be extended to infinite arrays. We apply SPP to relational modeling and the experimental results validate its merit compared to the state-of-the-arts.

We developed a new approach for the analysis of physiological time series. An iterative convolution filter is used to decompose the time series into various components. Statistics of these components are extracted as features to characterize the mechanisms underlying the time series. Motivated by the studies that show many normal physiological systems involve irregularity while the decrease of irregularity usually implies the abnormality, the statistics for "outliers" in the components are used as features measuring irregularity. Support vector machines are used to select the most relevant features that are able to differentiate the time series from normal and abnormal systems. This new approach is successfully used in the study of congestive heart failure by heart beat interval time series.

This paper is concerned with the question of reconstructing a vector in a finite-dimensional real Hilbert space when only the magnitudes of the coefficients of the vector under a redundant linear map are known. We analyze various Lipschitz bounds of the nonlinear analysis map and we establish theoretical performance bounds of any reconstruction algorithm. We show that robust and stable reconstruction requires additional redundancy than the critical threshold., Comment: 19 pages

We present an alternating augmented Lagrangian method for convex optimization problems where the cost function is the sum of two terms, one that is separable in the variable blocks, and a second that is separable in the difference between consecutive variable blocks. Examples of such problems include Fused Lasso estimation, total variation denoising, and multi-period portfolio optimization with transaction costs. In each iteration of our method, the first step involves separately optimizing over each variable block, which can be carried out in parallel. The second step is not separable in the variables, but can be carried out very efficiently. We apply the algorithm to segmentation of data based on changes inmean (l_1 mean filtering) or changes in variance (l_1 variance filtering). In a numerical example, we show that our implementation is around 10000 times faster compared with the generic optimization solver SDPT3.