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Sample reweighting is one of the most widely used methods for correcting the error of least squares learning algorithms in reproducing kernel Hilbert spaces (RKHS), that is caused by future data distributions that are different from the training data distribution. In practical situations, the sample weights are determined by values of the estimated Radon-Nikod\'ym derivative, of the future data distribution w.r.t.~the training data distribution. In this work, we review known error bounds for reweighted kernel regression in RKHS and obtain, by combination, novel results. We show under weak smoothness conditions, that the amount of samples, needed to achieve the same order of accuracy as in the standard supervised learning without differences in data distributions, is smaller than proven by state-of-the-art analyses.

Flow map learning (FML), in conjunction with deep neural networks (DNNs), has shown promises for data driven modeling of unknown dynamical systems. A remarkable feature of FML is that it is capable of producing accurate predictive models for partially observed systems, even when their exact mathematical models do not exist. In this paper, we present an overview of the FML framework, along with the important computational details for its successful implementation. We also present a set of well defined benchmark problems for learning unknown dynamical systems. All the numerical details of these problems are presented, along with their FML results, to ensure that the problems are accessible for cross-examination and the results are reproducible.

We suggest a simple Gaussian mixture model for data generation that complies with Feldman's long tail theory (2020). We demonstrate that a linear classifier cannot decrease the generalization error below a certain level in the proposed model, whereas a nonlinear classifier with a memorization capacity can. This confirms that for long-tailed distributions, rare training examples must be considered for optimal generalization to new data. Finally, we show that the performance gap between linear and nonlinear models can be lessened as the tail becomes shorter in the subpopulation frequency distribution, as confirmed by experiments on synthetic and real data., accepted to ECAI 2023

Deep Learning (DL) , a variant of the neural network algorithms originally proposed in the 1980s, has made surprising progress in Artificial Intelligence (AI), ranging from language translation, protein folding, autonomous cars, and more recently human-like language models (CHATbots), all that seemed intractable until very recently. Despite the growing use of Deep Learning (DL) networks, little is actually understood about the learning mechanisms and representations that makes these networks effective across such a diverse range of applications. Part of the answer must be the huge scale of the architecture and of course the large scale of the data, since not much has changed since 1987. But the nature of deep learned representations remain largely unknown. Unfortunately training sets with millions or billions of tokens have unknown combinatorics and Networks with millions or billions of hidden units cannot easily be visualized and their mechanisms cannot be easily revealed. In this paper, we explore these questions with a large (1.24M weights; VGG) DL in a novel high density sample task (5 unique tokens with at minimum 500 exemplars per token) which allows us to more carefully follow the emergence of category structure and feature construction. We use various visualization methods for following the emergence of the classification and the development of the coupling of feature detectors and structures that provide a type of graphical bootstrapping, From these results we harvest some basic observations of the learning dynamics of DL and propose a new theory of complex feature construction based on our results.

Many recent theoretical works on \emph{meta-learning} aim to achieve guarantees in leveraging similar representational structures from related tasks towards simplifying a target task. Importantly, the main aim in theory works on the subject is to understand the extent to which convergence rates -- in learning a common representation -- \emph{may scale with the number $N$ of tasks} (as well as the number of samples per task). First steps in this setting demonstrate this property when both the shared representation amongst tasks, and task-specific regression functions, are linear. This linear setting readily reveals the benefits of aggregating tasks, e.g., via averaging arguments. In practice, however, the representation is often highly nonlinear, introducing nontrivial biases in each task that cannot easily be averaged out as in the linear case. In the present work, we derive theoretical guarantees for meta-learning with nonlinear representations. In particular, assuming the shared nonlinearity maps to an infinite-dimensional RKHS, we show that additional biases can be mitigated with careful regularization that leverages the smoothness of task-specific regression functions

This article studies the Fisher-Rao gradient, also referred to as the natural gradient, of the evidence lower bound, the ELBO, which plays a crucial role within the theory of the Variational Autonecoder, the Helmholtz Machine and the Free Energy Principle. The natural gradient of the ELBO is related to the natural gradient of the Kullback-Leibler divergence from a target distribution, the prime objective function of learning. Based on invariance properties of gradients within information geometry, conditions on the underlying model are provided that ensure the equivalence of minimising the prime objective function and the maximisation of the ELBO.

Neural Persistence is a prominent measure for quantifying neural network complexity, proposed in the emerging field of topological data analysis in deep learning. In this work, however, we find both theoretically and empirically that the variance of network weights and spatial concentration of large weights are the main factors that impact neural persistence. Whilst this captures useful information for linear classifiers, we find that no relevant spatial structure is present in later layers of deep neural networks, making neural persistence roughly equivalent to the variance of weights. Additionally, the proposed averaging procedure across layers for deep neural networks does not consider interaction between layers. Based on our analysis, we propose an extension of the filtration underlying neural persistence to the whole neural network instead of single layers, which is equivalent to calculating neural persistence on one particular matrix. This yields our deep graph persistence measure, which implicitly incorporates persistent paths through the network and alleviates variance-related issues through standardisation. Code is available at https://github.com/ExplainableML/Deep-Graph-Persistence .

We propose new techniques for reducing communication in private federated learning without the need for setting or tuning compression rates. Our on-the-fly methods automatically adjust the compression rate based on the error induced during training, while maintaining provable privacy guarantees through the use of secure aggregation and differential privacy. Our techniques are provably instance-optimal for mean estimation, meaning that they can adapt to the ``hardness of the problem" with minimal interactivity. We demonstrate the effectiveness of our approach on real-world datasets by achieving favorable compression rates without the need for tuning., Accepted to ICML 2023

The Internet of Things (IoT) integrates more than billions of intelligent devices over the globe with the capability of communicating with other connected devices with little to no human intervention. IoT enables data aggregation and analysis on a large scale to improve life quality in many domains. In particular, data collected by IoT contain a tremendous amount of information for anomaly detection. The heterogeneous nature of IoT is both a challenge and an opportunity for cybersecurity. Traditional approaches in cybersecurity monitoring often require different kinds of data pre-processing and handling for various data types, which might be problematic for datasets that contain heterogeneous features. However, heterogeneous types of network devices can often capture a more diverse set of signals than a single type of device readings, which is particularly useful for anomaly detection. In this paper, we present a comprehensive study on using ensemble machine learning methods for enhancing IoT cybersecurity via anomaly detection. Rather than using one single machine learning model, ensemble learning combines the predictive power from multiple models, enhancing their predictive accuracy in heterogeneous datasets rather than using one single machine learning model. We propose a unified framework with ensemble learning that utilises Bayesian hyperparameter optimisation to adapt to a network environment that contains multiple IoT sensor readings. Experimentally, we illustrate their high predictive power when compared to traditional methods.

The aggregation of multiple opinions plays a crucial role in decision-making, such as in hiring and loan review, and in labeling data for supervised learning. Although majority voting and existing opinion aggregation models are effective for simple tasks, they are inappropriate for tasks without objectively true labels in which disagreements may occur. In particular, when voter attributes such as gender or race introduce bias into opinions, the aggregation results may vary depending on the composition of voter attributes. A balanced group of voters is desirable for fair aggregation results but may be difficult to prepare. In this study, we consider methods to achieve fair opinion aggregation based on voter attributes and evaluate the fairness of the aggregated results. To this end, we consider an approach that combines opinion aggregation models such as majority voting and the Dawid and Skene model (D&S model) with fairness options such as sample weighting. To evaluate the fairness of opinion aggregation, probabilistic soft labels are preferred over discrete class labels. First, we address the problem of soft label estimation without considering voter attributes and identify some issues with the D&S model. To address these limitations, we propose a new Soft D&S model with improved accuracy in estimating soft labels. Moreover, we evaluated the fairness of an opinion aggregation model, including Soft D&S, in combination with different fairness options using synthetic and semi-synthetic data. The experimental results suggest that the combination of Soft D&S and data splitting as a fairness option is effective for dense data, whereas weighted majority voting is effective for sparse data. These findings should prove particularly valuable in supporting decision-making by human and machine-learning models with balanced opinion aggregation.

Preference-based feedback is important for many applications where direct evaluation of a reward function is not feasible. A notable recent example arises in reinforcement learning from human feedback on large language models. For many of these applications, the cost of acquiring the human feedback can be substantial or even prohibitive. In this work, we take advantage of the fact that often the agent can choose contexts at which to obtain human feedback in order to most efficiently identify a good policy, and introduce the offline contextual dueling bandit setting. We give an upper-confidence-bound style algorithm for this setting and prove a regret bound. We also give empirical confirmation that this method outperforms a similar strategy that uses uniformly sampled contexts.

Performance of a pre-trained semantic segmentation model is likely to substantially decrease on data from a new domain. We show a pre-trained model can be adapted to unlabelled target domain data by calculating soft-label prototypes under the domain shift and making predictions according to the prototype closest to the vector with predicted class probabilities. The proposed adaptation procedure is fast, comes almost for free in terms of computational resources and leads to considerable performance improvements. We demonstrate the benefits of such label calibration on the highly-practical synthetic-to-real semantic segmentation problem., ICLR 2023 Workshop on Pitfalls of Limited Data and Computation for Trustworthy ML

A very popular model-agnostic technique for explaining predictive models is the SHapley Additive exPlanation (SHAP). The two most popular versions of SHAP are a conditional expectation version and an unconditional expectation version (the latter is also known as interventional SHAP). Except for tree-based methods, usually the unconditional version is used (for computational reasons). We provide a (surrogate) neural network approach which allows us to efficiently calculate the conditional version for both neural networks and other regression models, and which properly considers the dependence structure in the feature components. This proposal is also useful to provide drop1 and anova analyses in complex regression models which are similar to their generalized linear model (GLM) counterparts, and we provide a partial dependence plot (PDP) counterpart that considers the right dependence structure in the feature components., 24 pages, 9 figures

Source-free domain adaptation has become popular because of its practical usefulness and no need to access source data. However, the adaptation process still takes a considerable amount of time and is predominantly based on optimization that relies on back-propagation. In this work we present a simple feed-forward approach that challenges the need for back-propagation based adaptation. Our approach is based on computing prototypes of classes under the domain shift using a pre-trained model. It achieves strong improvements in accuracy compared to the pre-trained model and requires only a small fraction of time of existing domain adaptation methods., ECCV 2022 Workshop on Out of Distribution Generalization in Computer Vision (OOD-CV)

Gromov-Wasserstein distance has found many applications in machine learning due to its ability to compare measures across metric spaces and its invariance to isometric transformations. However, in certain applications, this invariance property can be too flexible, thus undesirable. Moreover, the Gromov-Wasserstein distance solely considers pairwise sample similarities in input datasets, disregarding the raw feature representations. We propose a new optimal transport-based distance, called Augmented Gromov-Wasserstein, that allows for some control over the level of rigidity to transformations. It also incorporates feature alignments, enabling us to better leverage prior knowledge on the input data for improved performance. We present theoretical insights into the proposed metric. We then demonstrate its usefulness for single-cell multi-omic alignment tasks and a transfer learning scenario in machine learning.

Bayesian nonparametric mixture models are widely used to cluster observations. However, one major drawback of the approach is that the estimated partition often presents unbalanced clusters' frequencies with only a few dominating clusters and a large number of sparsely-populated ones. This feature translates into results that are often uninterpretable unless we accept to ignore a relevant number of observations and clusters. Interpreting the posterior distribution as penalized likelihood, we show how the unbalance can be explained as a direct consequence of the cost functions involved in estimating the partition. In light of our findings, we propose a novel Bayesian estimator of the clustering configuration. The proposed estimator is equivalent to a post-processing procedure that reduces the number of sparsely-populated clusters and enhances interpretability. The procedure takes the form of entropy-regularization of the Bayesian estimate. While being computationally convenient with respect to alternative strategies, it is also theoretically justified as a correction to the Bayesian loss function used for point estimation and, as such, can be applied to any posterior distribution of clusters, regardless of the specific model used.

In a backdoor attack, an adversary inserts maliciously constructed backdoor examples into a training set to make the resulting model vulnerable to manipulation. Defending against such attacks typically involves viewing these inserted examples as outliers in the training set and using techniques from robust statistics to detect and remove them. In this work, we present a different approach to the backdoor attack problem. Specifically, we show that without structural information about the training data distribution, backdoor attacks are indistinguishable from naturally-occurring features in the data--and thus impossible to "detect" in a general sense. Then, guided by this observation, we revisit existing defenses against backdoor attacks and characterize the (often latent) assumptions they make and on which they depend. Finally, we explore an alternative perspective on backdoor attacks: one that assumes these attacks correspond to the strongest feature in the training data. Under this assumption (which we make formal) we develop a new primitive for detecting backdoor attacks. Our primitive naturally gives rise to a detection algorithm that comes with theoretical guarantees and is effective in practice., ICML 2023

In this paper, we introduce and analyze a variant of the Thompson sampling (TS) algorithm for contextual bandits. At each round, traditional TS requires samples from the current posterior distribution, which is usually intractable. To circumvent this issue, approximate inference techniques can be used and provide samples with distribution close to the posteriors. However, current approximate techniques yield to either poor estimation (Laplace approximation) or can be computationally expensive (MCMC methods, Ensemble sampling...). In this paper, we propose a new algorithm, Varational Inference Thompson sampling VITS, based on Gaussian Variational Inference. This scheme provides powerful posterior approximations which are easy to sample from, and is computationally efficient, making it an ideal choice for TS. In addition, we show that VITS achieves a sub-linear regret bound of the same order in the dimension and number of round as traditional TS for linear contextual bandit. Finally, we demonstrate experimentally the effectiveness of VITS on both synthetic and real world datasets.

To avoid failures on out-of-distribution data, recent works have sought to extract features that have a stable or invariant relationship with the label across domains, discarding the "spurious" or unstable features whose relationship with the label changes across domains. However, unstable features often carry complementary information about the label that could boost performance if used correctly in the test domain. Our main contribution is to show that it is possible to learn how to use these unstable features in the test domain without labels. In particular, we prove that pseudo-labels based on stable features provide sufficient guidance for doing so, provided that stable and unstable features are conditionally independent given the label. Based on this theoretical insight, we propose Stable Feature Boosting (SFB), an algorithm for: (i) learning a predictor that separates stable and conditionally-independent unstable features; and (ii) using the stable-feature predictions to adapt the unstable-feature predictions in the test domain. Theoretically, we prove that SFB can learn an asymptotically-optimal predictor without test-domain labels. Empirically, we demonstrate the effectiveness of SFB on real and synthetic data.

Recently, machine learning algorithms have been used remarkably to study the equilibrium phase transitions, however there are only a few works have been done using this technique in the nonequilibrium phase transitions. In this work, we use the supervised learning with the convolutional neural network (CNN) algorithm and unsupervised learning with the density-based spatial clustering of applications with noise (DBSCAN) algorithm to study the nonequilibrium phase transition in two models. We use CNN and DBSCAN in order to determine the critical points for directed bond percolation (bond DP) model and Domany-Kinzel cellular automaton (DK) model. Both models have been proven to have a nonequilibrium phase transition belongs to the directed percolation (DP) universality class. In the case of supervised learning we train CNN using the images which are generated from Monte Carlo simulations of directed bond percolation. We use that trained CNN in studding the phase transition for the two models. In the case of unsupervised learning, we train DBSCAN using the raw data of Monte Carlo simulations. In this case, we retrain DBSCAN at each time we change the model or lattice size. Our results from both algorithms show that, even for a very small values of lattice size, machine can predict the critical points accurately for both models. Finally, we mention to that, the value of the critical point we find here for bond DP model using CNN or DBSCAN is exactly the same value that has been found using transfer learning with a domain adversarial neural network (DANN) algorithm., 13 pages. 9 figures

Recommender systems are a ubiquitous feature of online platforms. Increasingly, they are explicitly tasked with increasing users' long-term satisfaction. In this context, we study a content exploration task, which we formalize as a multi-armed bandit problem with delayed rewards. We observe that there is an apparent trade-off in choosing the learning signal: Waiting for the full reward to become available might take several weeks, hurting the rate at which learning happens, whereas measuring short-term proxy rewards reflects the actual long-term goal only imperfectly. We address this challenge in two steps. First, we develop a predictive model of delayed rewards that incorporates all information obtained to date. Full observations as well as partial (short or medium-term) outcomes are combined through a Bayesian filter to obtain a probabilistic belief. Second, we devise a bandit algorithm that takes advantage of this new predictive model. The algorithm quickly learns to identify content aligned with long-term success by carefully balancing exploration and exploitation. We apply our approach to a podcast recommendation problem, where we seek to identify shows that users engage with repeatedly over two months. We empirically validate that our approach results in substantially better performance compared to approaches that either optimize for short-term proxies, or wait for the long-term outcome to be fully realized., Presented at the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD '23)

In this paper, we investigate the convergence properties of the stochastic gradient descent (SGD) method and its variants, especially in training neural networks built from nonsmooth activation functions. We develop a novel framework that assigns different timescales to stepsizes for updating the momentum terms and variables, respectively. Under mild conditions, we prove the global convergence of our proposed framework in both single-timescale and two-timescale cases. We show that our proposed framework encompasses a wide range of well-known SGD-type methods, including heavy-ball SGD, SignSGD, Lion, normalized SGD and clipped SGD. Furthermore, when the objective function adopts a finite-sum formulation, we prove the convergence properties for these SGD-type methods based on our proposed framework. In particular, we prove that these SGD-type methods find the Clarke stationary points of the objective function with randomly chosen stepsizes and initial points under mild assumptions. Preliminary numerical experiments demonstrate the high efficiency of our analyzed SGD-type methods., 30 pages

As causal ground truth is incredibly rare, causal discovery algorithms are commonly only evaluated on simulated data. This is concerning, given that simulations reflect common preconceptions about generating processes regarding noise distributions, model classes, and more. In this work, we propose a novel method for falsifying the output of a causal discovery algorithm in the absence of ground truth. Our key insight is that while statistical learning seeks stability across subsets of data points, causal learning should seek stability across subsets of variables. Motivated by this insight, our method relies on a notion of compatibility between causal graphs learned on different subsets of variables. We prove that detecting incompatibilities can falsify wrongly inferred causal relations due to violation of assumptions or errors from finite sample effects. Although passing such compatibility tests is only a necessary criterion for good performance, we argue that it provides strong evidence for the causal models whenever compatibility entails strong implications for the joint distribution. We also demonstrate experimentally that detection of incompatibilities can aid in causal model selection., 28 pages, 10 figures

Low-rank tensor analysis has received widespread attention with many practical applications. However, the tensor data are often contaminated by outliers or sample-specific corruptions. How to recover the tensor data that are corrupted by outliers and perform data clustering remains a challenging problem. This paper develops an outlier-robust tensor low-rank representation (OR-TLRR) method for simultaneous outlier detection and tensor data clustering based on the tensor singular value decomposition (t-SVD) algebraic framework. It is motivated by the recently proposed tensor-tensor product induced by invertible linear transforms that satisfy certain conditions. For tensor observations with arbitrary outlier corruptions, OR-TLRR has provable performance guarantee for exactly recovering the row space of clean data and detecting outliers under mild conditions. Moreover, an extension of OR-TLRR is also proposed to handle the case when parts of the data are missing. Finally, extensive experimental results on both synthetic and real data demonstrate the effectiveness of the proposed algorithms., 12 pages, 1 figure; preprint of a journal paper

We introduce a new class of adaptive importance samplers leveraging adaptive optimisation tools, which we term AdaOAIS. We build on Optimised Adaptive Importance Samplers (OAIS), a class of techniques that adapt proposals to improve the mean-squared error of the importance sampling estimators by parameterising the proposal and optimising the $\chi^2$-divergence between the target and the proposal. We show that a naive implementation of OAIS using stochastic gradient descent may lead to unstable estimators despite its convergence guarantees. To remedy this shortcoming, we instead propose to use adaptive optimisers (such as AdaGrad and Adam) to improve the stability of the OAIS. We provide convergence results for AdaOAIS in a similar manner to OAIS. We also provide empirical demonstration on a variety of examples and show that AdaOAIS lead to stable importance sampling estimators in practice., Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible

Uncertainty learning and quantification of models are crucial tasks to enhance the trustworthiness of the models. Importantly, the recent surge of generative language models (GLMs) emphasizes the need for reliable uncertainty quantification due to the concerns on generating hallucinated facts. In this paper, we propose to learn neural prediction set models that comes with the probably approximately correct (PAC) guarantee for quantifying the uncertainty of GLMs. Unlike existing prediction set models, which are parameterized by a scalar value, we propose to parameterize prediction sets via neural networks, which achieves more precise uncertainty quantification but still satisfies the PAC guarantee. We demonstrate the efficacy of our method on four types of language datasets and six types of models by showing that our method improves the quantified uncertainty by $63\%$ on average, compared to a standard baseline method.

In this paper, we carefully investigate how we can use multiple different Natural Language Processing techniques and methods in order to automatically recognize the main actions in sports events. We aim to extract insights by analyzing live sport commentaries from different sources and by classifying these major actions into different categories. We also study if sentiment analysis could help detect these main actions.

Since distribution shifts are common in real-world applications, there is a pressing need for developing prediction models that are robust against such shifts. Existing frameworks, such as empirical risk minimization or distributionally robust optimization, either lack generalizability for unseen distributions or rely on postulated distance measures. Alternatively, causality offers a data-driven and structural perspective to robust predictions. However, the assumptions necessary for causal inference can be overly stringent, and the robustness offered by such causal models often lacks flexibility. In this paper, we focus on causality-oriented robustness and propose Distributional Robustness via Invariant Gradients (DRIG), a method that exploits general additive interventions in training data for robust predictions against unseen interventions, and naturally interpolates between in-distribution prediction and causality. In a linear setting, we prove that DRIG yields predictions that are robust among a data-dependent class of distribution shifts. Furthermore, we show that our framework includes anchor regression (Rothenh\"ausler et al.\ 2021) as a special case, and that it yields prediction models that protect against more diverse perturbations. We extend our approach to the semi-supervised domain adaptation setting to further improve prediction performance. Finally, we empirically validate our methods on synthetic simulations and on single-cell data.

We consider the problem of learning a sparse graph underlying an undirected Gaussian graphical model, a key problem in statistical machine learning. Given $n$ samples from a multivariate Gaussian distribution with $p$ variables, the goal is to estimate the $p \times p$ inverse covariance matrix (aka precision matrix), assuming it is sparse (i.e., has a few nonzero entries). We propose GraphL0BnB, a new estimator based on an $\ell_0$-penalized version of the pseudolikelihood function, while most earlier approaches are based on the $\ell_1$-relaxation. Our estimator can be formulated as a convex mixed integer program (MIP) which can be difficult to compute at scale using off-the-shelf commercial solvers. To solve the MIP, we propose a custom nonlinear branch-and-bound (BnB) framework that solves node relaxations with tailored first-order methods. As a by-product of our BnB framework, we propose large-scale solvers for obtaining good primal solutions that are of independent interest. We derive novel statistical guarantees (estimation and variable selection) for our estimator and discuss how our approach improves upon existing estimators. Our numerical experiments on real/synthetic datasets suggest that our method can solve, to near-optimality, problem instances with $p = 10^4$ -- corresponding to a symmetric matrix of size $p \times p$ with $p^2/2$ binary variables. We demonstrate the usefulness of GraphL0BnB versus various state-of-the-art approaches on a range of datasets.

Our motivation is to shed light the performance of the widely popular "R-Learner." Like many other methods for estimating conditional average treatment effects (CATEs), R-Learning can be expressed as a weighted pseudo-outcome regression (POR). Previous comparisons of POR techniques have paid careful attention to the choice of pseudo-outcome transformation. However, we argue that the dominant driver of performance is actually the choice of weights. Specifically, we argue that R-Learning implicitly performs an inverse-variance weighted form of POR. These weights stabilize the regression and allow for convenient simplifications of bias terms.

We study bi-directional associative neural networks that, exposed to noisy examples of an extensive number of random archetypes, learn the latter (with or without the presence of a teacher) when the supplied information is enough: in this setting, learning is heteroassociative -- involving couples of patterns -- and it is achieved by reverberating the information depicted from the examples through the layers of the network. By adapting Guerra's interpolation technique, we provide a full statistical mechanical picture of supervised and unsupervised learning processes (at the replica symmetric level of description) obtaining analytically phase diagrams, thresholds for learning, a picture of the ground-state in plain agreement with Monte Carlo simulations and signal-to-noise outcomes. In the large dataset limit, the Kosko storage prescription as well as its statistical mechanical picture provided by Kurchan, Peliti, and Saber in the eighties is fully recovered. Computational advantages in dealing with information reverberation, rather than storage, are discussed for natural test cases. In particular, we show how this network admits an integral representation in terms of two coupled restricted Boltzmann machines, whose hidden layers are entirely built of by grand-mother neurons, to prove that by coupling solely these grand-mother neurons we can correlate the patterns they are related to: it is thus possible to recover Pavlov's Classical Conditioning by adding just one synapse among the correct grand-mother neurons (hence saving an extensive number of these links for further information storage w.r.t. the classical autoassociative setting).

In the absence of sensitive race and ethnicity data, researchers, regulators, and firms alike turn to proxies. In this paper, I train a Bidirectional Long Short-Term Memory (BiLSTM) model on a novel dataset of voter registration data from all 50 US states and create an ensemble that achieves up to 36.8% higher out of sample (OOS) F1 scores than the best performing machine learning models in the literature. Additionally, I construct the most comprehensive database of first and surname distributions in the US in order to improve the coverage and accuracy of Bayesian Improved Surname Geocoding (BISG) and Bayesian Improved Firstname Surname Geocoding (BIFSG). Finally, I provide the first high-quality benchmark dataset in order to fairly compare existing models and aid future model developers.

Colorectal cancer is a deadly disease that has become increasingly prevalent in recent years. Early detection is crucial for saving lives, but traditional diagnostic methods such as colonoscopy and biopsy have limitations. Colonoscopy cannot provide detailed information within the tissues affected by cancer, while biopsy involves tissue removal, which can be painful and invasive. In order to improve diagnostic efficiency and reduce patient suffering, we studied machine-learningbased approach for colorectal tissue classification that uses acoustic resolution photoacoustic microscopy (ARPAM). With this tool, we were able to classify benign and malignant tissue using multiple machine learning methods. Our results were analyzed both quantitatively and qualitatively to evaluate the effectiveness of our approach.

Ordinal scores occur commonly in medical imaging studies and in black-box forensic studies \citep{Phillips:2018}. To assess the accuracy of raters in the studies, one needs to estimate the receiver operating characteristic (ROC) curve while accounting for covariates of raters. In this paper, we propose a covariate-adjusted homogeneity test to determine differences in accuracy among multiple rater groups. We derived the theoretical results of the proposed test and conducted extensive simulation studies to evaluate the finite sample performance of the proposed test. Our proposed test is applied to a face recognition study to identify statistically significant differences among five participant groups.

High-dimensional clinical data have become invaluable resources for genetic studies, due to their accessibility in biobank-scale datasets and the development of high performance modeling techniques especially using deep learning. Recent work has shown that low dimensional embeddings of these clinical data learned by variational autoencoders (VAE) can be used for genome-wide association studies and polygenic risk prediction. In this work, we consider multiple unsupervised learning methods for learning disentangled representations, namely autoencoders, VAE, beta-VAE, and FactorVAE, in the context of genetic association studies. Using spirograms from UK Biobank as a running example, we observed improvements in the number of genome-wide significant loci, heritability, and performance of polygenic risk scores for asthma and chronic obstructive pulmonary disease by using FactorVAE or beta-VAE, compared to standard VAE or non-variational autoencoders. FactorVAEs performed effectively across multiple values of the regularization hyperparameter, while beta-VAEs were much more sensitive to the hyperparameter values., Accepted to the 2023 ICML Workshop on Computational Biology. Honolulu, Hawaii, USA, 2023

In this paper, we propose an online convex optimization method with two different levels of adaptivity. On a higher level, our method is agnostic to the specific type and curvature of the loss functions, while at a lower level, it can exploit the niceness of the environments and attain problem-dependent guarantees. To be specific, we obtain $\mathcal{O}(\ln V_T)$, $\mathcal{O}(d \ln V_T)$ and $\hat{\mathcal{O}}(\sqrt{V_T})$ regret bounds for strongly convex, exp-concave and convex loss functions, respectively, where $d$ is the dimension, $V_T$ denotes problem-dependent gradient variations and $\hat{\mathcal{O}}(\cdot)$-notation omits logarithmic factors on $V_T$. Our result finds broad implications and applications. It not only safeguards the worst-case guarantees, but also implies the small-loss bounds in analysis directly. Besides, it draws deep connections with adversarial/stochastic convex optimization and game theory, further validating its practical potential. Our method is based on a multi-layer online ensemble incorporating novel ingredients, including carefully-designed optimism for unifying diverse function types and cascaded corrections for algorithmic stability. Remarkably, despite its multi-layer structure, our algorithm necessitates only one gradient query per round, making it favorable when the gradient evaluation is time-consuming. This is facilitated by a novel regret decomposition equipped with customized surrogate losses.

Methicillin-resistant Staphylococcus aureus (MRSA) is a type of bacteria resistant to certain antibiotics, making it difficult to prevent MRSA infections. Among decades of efforts to conquer infectious diseases caused by MRSA, many studies have been proposed to estimate the causal effects of close contact (treatment) on MRSA infection (outcome) from observational data. In this problem, the treatment assignment mechanism plays a key role as it determines the patterns of missing counterfactuals -- the fundamental challenge of causal effect estimation. Most existing observational studies for causal effect learning assume that the treatment is assigned individually for each unit. However, on many occasions, the treatments are pairwisely assigned for units that are connected in graphs, i.e., the treatments of different units are entangled. Neglecting the entangled treatments can impede the causal effect estimation. In this paper, we study the problem of causal effect estimation with treatment entangled in a graph. Despite a few explorations for entangled treatments, this problem still remains challenging due to the following challenges: (1) the entanglement brings difficulties in modeling and leveraging the unknown treatment assignment mechanism; (2) there may exist hidden confounders which lead to confounding biases in causal effect estimation; (3) the observational data is often time-varying. To tackle these challenges, we propose a novel method NEAT, which explicitly leverages the graph structure to model the treatment assignment mechanism, and mitigates confounding biases based on the treatment assignment modeling. We also extend our method into a dynamic setting to handle time-varying observational data. Experiments on both synthetic datasets and a real-world MRSA dataset validate the effectiveness of the proposed method, and provide insights for future applications.

Fairness-aware machine learning has attracted a surge of attention in many domains, such as online advertising, personalized recommendation, and social media analysis in web applications. Fairness-aware machine learning aims to eliminate biases of learning models against certain subgroups described by certain protected (sensitive) attributes such as race, gender, and age. Among many existing fairness notions, counterfactual fairness is a popular notion defined from a causal perspective. It measures the fairness of a predictor by comparing the prediction of each individual in the original world and that in the counterfactual worlds in which the value of the sensitive attribute is modified. A prerequisite for existing methods to achieve counterfactual fairness is the prior human knowledge of the causal model for the data. However, in real-world scenarios, the underlying causal model is often unknown, and acquiring such human knowledge could be very difficult. In these scenarios, it is risky to directly trust the causal models obtained from information sources with unknown reliability and even causal discovery methods, as incorrect causal models can consequently bring biases to the predictor and lead to unfair predictions. In this work, we address the problem of counterfactually fair prediction from observational data without given causal models by proposing a novel framework CLAIRE. Specifically, under certain general assumptions, CLAIRE effectively mitigates the biases from the sensitive attribute with a representation learning framework based on counterfactual data augmentation and an invariant penalty. Experiments conducted on both synthetic and real-world datasets validate the superiority of CLAIRE in both counterfactual fairness and prediction performance.

This work is concerned with the use of Gaussian surrogate models for Bayesian inverse problems associated with linear partial differential equations. A particular focus is on the regime where only a small amount of training data is available. In this regime the type of Gaussian prior used is of critical importance with respect to how well the surrogate model will perform in terms of Bayesian inversion. We extend the framework of Raissi et. al. (2017) to construct PDE-informed Gaussian priors that we then use to construct different approximate posteriors. A number of different numerical experiments illustrate the superiority of the PDE-informed Gaussian priors over more traditional priors.

Corruption is frequently observed in collected data and has been extensively studied in machine learning under different corruption models. Despite this, there remains a limited understanding of how these models relate such that a unified view of corruptions and their consequences on learning is still lacking. In this work, we formally analyze corruption models at the distribution level through a general, exhaustive framework based on Markov kernels. We highlight the existence of intricate joint and dependent corruptions on both labels and attributes, which are rarely touched by existing research. Further, we show how these corruptions affect standard supervised learning by analyzing the resulting changes in Bayes Risk. Our findings offer qualitative insights into the consequences of "more complex" corruptions on the learning problem, and provide a foundation for future quantitative comparisons. Applications of the framework include corruption-corrected learning, a subcase of which we study in this paper by theoretically analyzing loss correction with respect to different corruption instances., 42 pages

Covariate shift in regression problems and the associated distribution mismatch between training and test data is a commonly encountered phenomenon in machine learning. In this paper, we extend recent results on nonparametric convergence rates for i.i.d. data to Markovian dependence structures. We demonstrate that under H\"older smoothness assumptions on the regression function, convergence rates for the generalization risk of a Nadaraya-Watson kernel estimator are determined by the similarity between the invariant distributions associated to source and target Markov chains. The similarity is explicitly captured in terms of a bandwidth-dependent similarity measure recently introduced in Pathak, Ma and Wainwright [ICML, 2022]. Precise convergence rates are derived for the particular cases of finite Markov chains and spectral gap Markov chains for which the similarity measure between their invariant distributions grows polynomially with decreasing bandwidth. For the latter, we extend the notion of a distribution transfer exponent from Kpotufe and Martinet [Ann. Stat., 49(6), 2021] to kernel transfer exponents of uniformly ergodic Markov chains in order to generate a rich class of Markov kernel pairs for which convergence guarantees for the covariate shift problem can be formulated.

Interpretability is a crucial aspect of machine learning models that enables humans to understand and trust the decision-making process of these models. In many real-world applications, the interpretability of models is essential for legal, ethical, and practical reasons. For instance, in the banking domain, interpretability is critical for lenders and borrowers to understand the reasoning behind the acceptance or rejection of loan applications as per fair lending laws. However, achieving interpretability in machine learning models is challenging, especially for complex high-performance models. Hence Explainable Boosting Machines (EBMs) have been gaining popularity due to their interpretable and high-performance nature in various prediction tasks. However, these models can suffer from issues such as spurious interactions with redundant features and single-feature dominance across all interactions, which can affect the interpretability and reliability of the model's predictions. In this paper, we explore novel approaches to address these issues by utilizing alternate Cross-feature selection, ensemble features and model configuration alteration techniques. Our approach involves a multi-step feature selection procedure that selects a set of candidate features, ensemble features and then benchmark the same using the EBM model. We evaluate our method on three benchmark datasets and show that the alternate techniques outperform vanilla EBM methods, while providing better interpretability and feature selection stability, and improving the model's predictive performance. Moreover, we show that our approach can identify meaningful interactions and reduce the dominance of single features in the model's predictions, leading to more reliable and interpretable models. Index Terms- Interpretability, EBM's, ensemble, feature selection.

In generative modeling, numerous successful approaches leverage a low-dimensional latent space, e.g., Stable Diffusion models the latent space induced by an encoder and generates images through a paired decoder. Although the selection of the latent space is empirically pivotal, determining the optimal choice and the process of identifying it remain unclear. In this study, we aim to shed light on this under-explored topic by rethinking the latent space from the perspective of model complexity. Our investigation starts with the classic generative adversarial networks (GANs). Inspired by the GAN training objective, we propose a novel "distance" between the latent and data distributions, whose minimization coincides with that of the generator complexity. The minimizer of this distance is characterized as the optimal data-dependent latent that most effectively capitalizes on the generator's capacity. Then, we consider parameterizing such a latent distribution by an encoder network and propose a two-stage training strategy called Decoupled Autoencoder (DAE), where the encoder is only updated in the first stage with an auxiliary decoder and then frozen in the second stage while the actual decoder is being trained. DAE can improve the latent distribution and as a result, improve the generative performance. Our theoretical analyses are corroborated by comprehensive experiments on various models such as VQGAN and Diffusion Transformer, where our modifications yield significant improvements in sample quality with decreased model complexity., TL;DR: This work characterizes the optimal latent distribution for generative models from the perspective of minimizing model complexity and proposes a two-stage training scheme that achieves practical improvements on GAN, VQGAN and DiT

Many real-world processes have complex tail dependence structures that cannot be characterized using classical Gaussian processes. More flexible spatial extremes models such as Gaussian scale mixtures and single-station conditioning models exhibit appealing extremal dependence properties but are often exceedingly prohibitive to fit and simulate from. In this paper, we develop a new spatial extremes model that has flexible and non-stationary dependence properties, and we integrate it in the encoding-decoding structure of a variational autoencoder (extVAE). The extVAE can be used as a spatio-temporal emulator that characterizes the distribution of potential mechanistic model output states and produces outputs that have the same properties as the inputs, especially in the tail. Through extensive simulation studies, we show that our extVAE is vastly more time-efficient than traditional Bayesian inference while also outperforming many spatial extremes models with a stationary dependence structure. To further demonstrate the computational power of the extVAE, we analyze a high-resolution satellite-derived dataset of sea surface temperature in the Red Sea, which includes daily measurements at 16703 grid cells., 27 pages, 13 figures

High spatial resolution wind data are essential for a wide range of applications in climate, oceanographic and meteorological studies. Large-scale spatial interpolation or downscaling of bivariate wind fields having velocity in two dimensions is a challenging task because wind data tend to be non-Gaussian with high spatial variability and heterogeneity. In spatial statistics, cokriging is commonly used for predicting bivariate spatial fields. However, the cokriging predictor is not optimal except for Gaussian processes. Additionally, cokriging is computationally prohibitive for large datasets. In this paper, we propose a method, called bivariate DeepKriging, which is a spatially dependent deep neural network (DNN) with an embedding layer constructed by spatial radial basis functions for bivariate spatial data prediction. We then develop a distribution-free uncertainty quantification method based on bootstrap and ensemble DNN. Our proposed approach outperforms the traditional cokriging predictor with commonly used covariance functions, such as the linear model of co-regionalization and flexible bivariate Mat\'ern covariance. We demonstrate the computational efficiency and scalability of the proposed DNN model, with computations that are, on average, 20 times faster than those of conventional techniques. We apply the bivariate DeepKriging method to the wind data over the Middle East region at 506,771 locations. The prediction performance of the proposed method is superior over the cokriging predictors and dramatically reduces computation time.

This paper studies the qualitative behavior and robustness of two variants of Minimal Random Code Learning (MIRACLE) used to compress variational Bayesian neural networks. MIRACLE implements a powerful, conditionally Gaussian variational approximation for the weight posterior $Q_{\mathbf{w}}$ and uses relative entropy coding to compress a weight sample from the posterior using a Gaussian coding distribution $P_{\mathbf{w}}$. To achieve the desired compression rate, $D_{\mathrm{KL}}[Q_{\mathbf{w}} \Vert P_{\mathbf{w}}]$ must be constrained, which requires a computationally expensive annealing procedure under the conventional mean-variance (Mean-Var) parameterization for $Q_{\mathbf{w}}$. Instead, we parameterize $Q_{\mathbf{w}}$ by its mean and KL divergence from $P_{\mathbf{w}}$ to constrain the compression cost to the desired value by construction. We demonstrate that variational training with Mean-KL parameterization converges twice as fast and maintains predictive performance after compression. Furthermore, we show that Mean-KL leads to more meaningful variational distributions with heavier tails and compressed weight samples which are more robust to pruning., ICML Neural Compression Workshop 2023

Quadratic programming is a fundamental problem in the field of convex optimization. Many practical tasks can be formulated as quadratic programming, for example, the support vector machine (SVM). Linear SVM is one of the most popular tools over the last three decades in machine learning before deep learning method dominating. In general, a quadratic program has input size $\Theta(n^2)$ (where $n$ is the number of variables), thus takes $\Omega(n^2)$ time to solve. Nevertheless, quadratic programs coming from SVMs has input size $O(n)$, allowing the possibility of designing nearly-linear time algorithms. Two important classes of SVMs are programs admitting low-rank kernel factorizations and low-treewidth programs. Low-treewidth convex optimization has gained increasing interest in the past few years (e.g.~linear programming [Dong, Lee and Ye 2021] and semidefinite programming [Gu and Song 2022]). Therefore, an important open question is whether there exist nearly-linear time algorithms for quadratic programs with these nice structures. In this work, we provide the first nearly-linear time algorithm for solving quadratic programming with low-rank factorization or low-treewidth, and a small number of linear constraints. Our results imply nearly-linear time algorithms for low-treewidth or low-rank SVMs., Comment: arXiv admin note: text overlap with arXiv:2211.06033

For any graph $G$ having $n$ vertices and its automorphism group $\textrm{Aut}(G)$, we provide a full characterisation of all of the possible $\textrm{Aut}(G)$-equivariant neural networks whose layers are some tensor power of $\mathbb{R}^{n}$. In particular, we find a spanning set of matrices for the learnable, linear, $\textrm{Aut}(G)$-equivariant layer functions between such tensor power spaces in the standard basis of $\mathbb{R}^{n}$., 25 pages

When artificial neural networks have demonstrated exceptional practical success in a variety of domains, investigations into their theoretical characteristics, such as their approximation power, statistical properties, and generalization performance, have made significant strides. In this paper, we construct a novel theory for understanding the effectiveness of neural networks by discovering the mystery underlying a common practice during neural network model construction: sample splitting. Our theory demonstrates that, the optimal hyperparameters derived from sample splitting can enable a neural network model that asymptotically minimizes the prediction risk. We conduct extensive experiments across different application scenarios and network architectures, and the results manifest our theory's effectiveness., 32 pages, 5 figures

Load forecasting is of great significance in the power industry as it can provide a reference for subsequent tasks such as power grid dispatch, thus bringing huge economic benefits. However, there are many differences between load forecasting and traditional time series forecasting. On the one hand, load forecasting aims to minimize the cost of subsequent tasks such as power grid dispatch, rather than simply pursuing prediction accuracy. On the other hand, the load is largely influenced by many external factors, such as temperature or calendar variables. In addition, the scale of predictions (such as building-level loads and aggregated-level loads) can also significantly impact the predicted results. In this paper, we provide a comprehensive load forecasting archive, which includes load domain-specific feature engineering to help forecasting models better model load data. In addition, different from the traditional loss function which only aims for accuracy, we also provide a method to customize the loss function based on the forecasting error, integrating it into our forecasting framework. Based on this, we conducted extensive experiments on load data at different levels, providing a reference for researchers to compare different load forecasting models.