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This paper characterizes the impact of covariates serial dependence on the non-asymptotic estimation error bound of penalized regressions (PRs). Focusing on the direct relationship between the degree of cross-correlation of covariates and the estimation error bound of PRs, we show that orthogonal or weakly cross-correlated stationary AR processes can exhibit high spurious correlations caused by serial dependence. In this respect, we study analytically the density of sample cross-correlations in the case of two orthogonal Gaussian AR(1) processes. Our results are validated by an extensive simulation study. Furthermore, we introduce a new procedure to remedy spurious correlations in a time series regime, applying PRs to pre-whitened (ARMA filter) time series. We show that under mild assumptions our procedure allows both to reduce the estimation error and to develop an effective forecasting strategy. The estimation accuracy of our proposal is validated by means of simulations and an empirical application based on a large monthly macroeconomic data relative to the Euro Area economy.

The success of deep learning is largely due to the availability of large amounts of training data that cover a wide range of examples of a particular concept or meaning. In the field of medicine, having a diverse set of training data on a particular disease can lead to the development of a model that is able to accurately predict the disease. However, despite the potential benefits, there have not been significant advances in image-based diagnosis due to a lack of high-quality annotated data. This article highlights the importance of using a data-centric approach to improve the quality of data representations, particularly in cases where the available data is limited. To address this "small-data" issue, we discuss four methods for generating and aggregating training data: data augmentation, transfer learning, federated learning, and GANs (generative adversarial networks). We also propose the use of knowledge-guided GANs to incorporate domain knowledge in the training data generation process. With the recent progress in large pre-trained language models, we believe it is possible to acquire high-quality knowledge that can be used to improve the effectiveness of knowledge-guided generative methods.

We develop methods for reducing the dimensionality of large data sets, common in biomedical applications. Learning about patients using genetic data often includes more features than observations, which makes direct supervised learning difficult. One method of reducing the feature space is to use latent Dirichlet allocation to group genetic variants in an unsupervised manner. Latent Dirichlet allocation describes a patient as a mixture of topics corresponding to genetic variants. This can be generalized as a Bayesian tensor decomposition to account for multiple feature variables. Our most significant contributions are with hierarchical topic modeling. We design distinct methods of incorporating hierarchical topic modeling, based on nested Chinese restaurant processes and Pachinko Allocation Machine, into Bayesian tensor decomposition. We apply these models to examine patients with one of four common types of cancer (breast, lung, prostate, and colorectal) and siblings with and without autism spectrum disorder. We linked the genes with their biological pathways and combine this information into a tensor of patients, counts of their genetic variants, and the genes' membership in pathways. We find that our trained models outperform baseline models, with respect to coherence, by up to 40%.

Autoencoders are a popular model in many branches of machine learning and lossy data compression. However, their fundamental limits, the performance of gradient methods and the features learnt during optimization remain poorly understood, even in the two-layer setting. In fact, earlier work has considered either linear autoencoders or specific training regimes (leading to vanishing or diverging compression rates). Our paper addresses this gap by focusing on non-linear two-layer autoencoders trained in the challenging proportional regime in which the input dimension scales linearly with the size of the representation. Our results characterize the minimizers of the population risk, and show that such minimizers are achieved by gradient methods; their structure is also unveiled, thus leading to a concise description of the features obtained via training. For the special case of a sign activation function, our analysis establishes the fundamental limits for the lossy compression of Gaussian sources via (shallow) autoencoders. Finally, while the results are proved for Gaussian data, numerical simulations on standard datasets display the universality of the theoretical predictions.

Deep neural networks (DNNs) are known to be vulnerable to both backdoor attacks as well as adversarial attacks. In the literature, these two types of attacks are commonly treated as distinct problems and solved separately, since they belong to training-time and inference-time attacks respectively. However, in this paper we find an intriguing connection between them: for a model planted with backdoors, we observe that its adversarial examples have similar behaviors as its triggered images, i.e., both activate the same subset of DNN neurons. It indicates that planting a backdoor into a model will significantly affect the model's adversarial examples. Based on these observations, a novel Progressive Backdoor Erasing (PBE) algorithm is proposed to progressively purify the infected model by leveraging untargeted adversarial attacks. Different from previous backdoor defense methods, one significant advantage of our approach is that it can erase backdoor even when the clean extra dataset is unavailable. We empirically show that, against 5 state-of-the-art backdoor attacks, our PBE can effectively erase the backdoor without obvious performance degradation on clean samples and significantly outperforms existing defense methods.

In 1954, Alston S. Householder published Principles of Numerical Analysis, one of the first modern treatments on matrix decomposition that favored a (block) LU decomposition-the factorization of a matrix into the product of lower and upper triangular matrices. And now, matrix decomposition has become a core technology in machine learning, largely due to the development of the back propagation algorithm in fitting a neural network. The sole aim of this survey is to give a self-contained introduction to concepts and mathematical tools in numerical linear algebra and matrix analysis in order to seamlessly introduce matrix decomposition techniques and their applications in subsequent sections. However, we clearly realize our inability to cover all the useful and interesting results concerning matrix decomposition and given the paucity of scope to present this discussion, e.g., the separated analysis of the Euclidean space, Hermitian space, Hilbert space, and things in the complex domain. We refer the reader to literature in the field of linear algebra for a more detailed introduction to the related fields.

Hierarchical structures are popular in recent vision transformers, however, they require sophisticated designs and massive datasets to work well. In this paper, we explore the idea of nesting basic local transformers on non-overlapping image blocks and aggregating them in a hierarchical way. We find that the block aggregation function plays a critical role in enabling cross-block non-local information communication. This observation leads us to design a simplified architecture that requires minor code changes upon the original vision transformer. The benefits of the proposed judiciously-selected design are threefold: (1) NesT converges faster and requires much less training data to achieve good generalization on both ImageNet and small datasets like CIFAR; (2) when extending our key ideas to image generation, NesT leads to a strong decoder that is 8$\times$ faster than previous transformer-based generators; and (3) we show that decoupling the feature learning and abstraction processes via this nested hierarchy in our design enables constructing a novel method (named GradCAT) for visually interpreting the learned model. Source code is available //github.com/google-research/nested-transformer.

Since hardware resources are limited, the objective of training deep learning models is typically to maximize accuracy subject to the time and memory constraints of training and inference. We study the impact of model size in this setting, focusing on Transformer models for NLP tasks that are limited by compute: self-supervised pretraining and high-resource machine translation. We first show that even though smaller Transformer models execute faster per iteration, wider and deeper models converge in significantly fewer steps. Moreover, this acceleration in convergence typically outpaces the additional computational overhead of using larger models. Therefore, the most compute-efficient training strategy is to counterintuitively train extremely large models but stop after a small number of iterations. This leads to an apparent trade-off between the training efficiency of large Transformer models and the inference efficiency of small Transformer models. However, we show that large models are more robust to compression techniques such as quantization and pruning than small models. Consequently, one can get the best of both worlds: heavily compressed, large models achieve higher accuracy than lightly compressed, small models.

This work considers the question of how convenient access to copious data impacts our ability to learn causal effects and relations. In what ways is learning causality in the era of big data different from -- or the same as -- the traditional one? To answer this question, this survey provides a comprehensive and structured review of both traditional and frontier methods in learning causality and relations along with the connections between causality and machine learning. This work points out on a case-by-case basis how big data facilitates, complicates, or motivates each approach.

Causal inference is a critical research topic across many domains, such as statistics, computer science, education, public policy and economics, for decades. Nowadays, estimating causal effect from observational data has become an appealing research direction owing to the large amount of available data and low budget requirement, compared with randomized controlled trials. Embraced with the rapidly developed machine learning area, various causal effect estimation methods for observational data have sprung up. In this survey, we provide a comprehensive review of causal inference methods under the potential outcome framework, one of the well known causal inference framework. The methods are divided into two categories depending on whether they require all three assumptions of the potential outcome framework or not. For each category, both the traditional statistical methods and the recent machine learning enhanced methods are discussed and compared. The plausible applications of these methods are also presented, including the applications in advertising, recommendation, medicine and so on. Moreover, the commonly used benchmark datasets as well as the open-source codes are also summarized, which facilitate researchers and practitioners to explore, evaluate and apply the causal inference methods.