Latent factor model estimation typically relies on either using domain knowledge to manually pick several observed covariates as factor proxies, or purely conducting multivariate analysis such as principal component analysis. However, the former approach may suffer from the bias while the latter can not incorporate additional information. We propose to bridge these two approaches while allowing the number of factor proxies to diverge, and hence make the latent factor model estimation robust, flexible, and statistically more accurate. As a bonus, the number of factors is also allowed to grow. At the heart of our method is a penalized reduced rank regression to combine information. To further deal with heavy-tailed data, a computationally attractive penalized robust reduced rank regression method is proposed. We establish faster rates of convergence compared with the benchmark. Extensive simulations and real examples are used to illustrate the advantages.
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We study the problem of inferring heterogeneous treatment effects (HTEs) from time-to-event data in the presence of competing events. Albeit its great practical relevance, this problem has received little attention compared to its counterparts studying HTE estimation without time-to-event data or competing events. We take an outcome modeling approach to estimating HTEs, and consider how and when existing prediction models for time-to-event data can be used as plug-in estimators for potential outcomes. We then investigate whether competing events present new challenges for HTE estimation -- in addition to the standard confounding problem --, and find that, because there are multiple definitions of causal effects in this setting -- namely total, direct and separable effects --, competing events can act as an additional source of covariate shift depending on the desired treatment effect interpretation and associated estimand. We theoretically analyze and empirically illustrate when and how these challenges play a role when using generic machine learning prediction models for the estimation of HTEs.
When deployed for risk-sensitive tasks, deep neural networks must include an uncertainty estimation mechanism. Here we examine the relationship between deep architectures and their respective training regimes, with their corresponding selective prediction and uncertainty estimation performance. We consider some of the most popular estimation performance metrics previously proposed including AUROC, ECE, AURC as well as coverage for selective accuracy constraint. We present a novel and comprehensive study of selective prediction and the uncertainty estimation performance of 523 existing pretrained deep ImageNet classifiers that are available in popular repositories. We identify numerous and previously unknown factors that affect uncertainty estimation and examine the relationships between the different metrics. We find that distillation-based training regimes consistently yield better uncertainty estimations than other training schemes such as vanilla training, pretraining on a larger dataset and adversarial training. Moreover, we find a subset of ViT models that outperform any other models in terms of uncertainty estimation performance. For example, we discovered an unprecedented 99% top-1 selective accuracy on ImageNet at 47% coverage (and 95% top-1 accuracy at 80%) for a ViT model, whereas a competing EfficientNet-V2-XL cannot obtain these accuracy constraints at any level of coverage. Our companion paper, also published in ICLR 2023 (A framework for benchmarking class-out-of-distribution detection and its application to ImageNet), examines the performance of these classifiers in a class-out-of-distribution setting.
Calibration weighting has been widely used to correct selection biases in non-probability sampling, missing data, and causal inference. The main idea is to calibrate the biased sample to the benchmark by adjusting the subject weights. However, hard calibration can produce enormous weights when an exact calibration is enforced on a large set of extraneous covariates. This article proposes a soft calibration scheme, in which the outcome and the selection indicator follow mixed-effects models. The scheme imposes an exact calibration on the fixed effects and an approximate calibration on the random effects. On the one hand, our soft calibration has an intrinsic connection with best linear unbiased prediction, which results in a more efficient estimation compared to hard calibration. On the other hand, soft calibration weighting estimation can be envisioned as penalized propensity score weight estimation, with the penalty term motivated by the mixed-effects structure. The asymptotic distribution and a valid variance estimator are derived for soft calibration. We demonstrate the superiority of the proposed estimator over other competitors in simulation studies and a real-data application.
A crucial assumption underlying the most current theory of machine learning is that the training distribution is identical to the test distribution. However, this assumption may not hold in some real-world applications. In this paper, we develop a learning model based on principles of information theory by minimizing the worst-case loss at prescribed levels of uncertainty. We reformulate the empirical estimation of the risk functional and the distribution deviation constraint based on the importance sampling method. The objective of the proposed approach is to minimize the loss under maximum degradation and hence the resulting problem is a minimax problem which can be converted to an unconstrained minimum problem using the Lagrange method with the Lagrange multiplier $T$. We reveal that the minimization of the objective function under logarithmic transformation is equivalent to the minimization of the p-norm loss with $p=\frac{1}{T}$. We applied the proposed model to the face verification task on Racial Faces in the Wild datasets and showed that the proposed model performs better under large distribution deviations.
Solving inverse problems is central to a variety of important applications, such as biomedical image reconstruction and non-destructive testing. These problems are characterized by the sensitivity of direct solution methods with respect to data perturbations. To stabilize the reconstruction process, regularization methods have to be employed. Well-known regularization methods are based on frame expansions, such as the wavelet-vaguelette (WVD) decomposition, which are well adapted to the underlying signal class and the forward model and furthermore allow efficient implementation. However, it is well known that the lack of translational invariance of wavelets and related systems leads to specific artifacts in the reconstruction. To overcome this problem, in this paper we introduce and analyze the translation invariant diagonal frame decomposition (TI-DFD) of linear operators as a novel concept generalizing the SVD. We characterize ill-posedness via the TI-DFD and prove that a TI-DFD combined with a regularizing filter leads to a convergent regularization method with optimal convergence rates. As illustrative example, we construct a wavelet-based TI-DFD for one-dimensional integration, where we also investigate our approach numerically. The results indicate that filtered TI-DFDs eliminate the typical wavelet artifacts when using standard wavelets and provide a fast, accurate, and stable solution scheme for inverse problems.
Total correlation (TC) is a fundamental concept in information theory that measures statistical dependency among multiple random variables. Recently, TC has shown noticeable effectiveness as a regularizer in many learning tasks, where the correlation among multiple latent embeddings requires to be jointly minimized or maximized. However, calculating precise TC values is challenging, especially when the closed-form distributions of embedding variables are unknown. In this paper, we introduce a unified framework to estimate total correlation values with sample-based mutual information (MI) estimators. More specifically, we discover a relation between TC and MI and propose two types of calculation paths (tree-like and line-like) to decompose TC into MI terms. With each MI term being bounded, the TC values can be successfully estimated. Further, we provide theoretical analyses concerning the statistical consistency of the proposed TC estimators. Experiments are presented on both synthetic and real-world scenarios, where our estimators demonstrate effectiveness in all TC estimation, minimization, and maximization tasks. The code is available at //github.com/Linear95/TC-estimation.
We study the approximability of the four-vertex model, a special case of the six-vertex model.We prove that, despite being NP-hard to approximate in the worst case, the four-vertex model admits a fully polynomial randomized approximation scheme (FPRAS) when the input satisfies certain linear equation system.The FPRAS is given by a Markov chain called the worm process whose state space and rapid mixing rely on the solution of the linear equation system.This is the first attempt to design an FPRAS for the six-vertex model with unwinable constraint functions.Furthermore, we consider the application of this technique on planar graphs to give efficient sampling algorithms.
In this paper, we consider the task of clustering a set of individual time series while modeling each cluster, that is, model-based time series clustering. The task requires a parametric model with sufficient flexibility to describe the dynamics in various time series. To address this problem, we propose a novel model-based time series clustering method with mixtures of linear Gaussian state space models, which have high flexibility. The proposed method uses a new expectation-maximization algorithm for the mixture model to estimate the model parameters, and determines the number of clusters using the Bayesian information criterion. Experiments on a simulated dataset demonstrate the effectiveness of the method in clustering, parameter estimation, and model selection. The method is applied to real datasets commonly used to evaluate time series clustering methods. Results showed that the proposed method produces clustering results that are as accurate or more accurate than those obtained using previous methods.
In large datasets, it is hard to discover and analyze structure. It is thus common to introduce tags or keywords for the items. In applications, such datasets are then filtered based on these tags. Still, even medium-sized datasets with a few tags result in complex and for humans hard-to-navigate systems. In this work, we adopt the method of ordinal factor analysis to address this problem. An ordinal factor arranges a subset of the tags in a linear order based on their underlying structure. A complete ordinal factorization, which consists of such ordinal factors, precisely represents the original dataset. Based on such an ordinal factorization, we provide a way to discover and explain relationships between different items and attributes in the dataset. However, computing even just one ordinal factor of high cardinality is computationally complex. We thus propose the greedy algorithm in this work. This algorithm extracts ordinal factors using already existing fast algorithms developed in formal concept analysis. Then, we leverage to propose a comprehensive way to discover relationships in the dataset. We furthermore introduce a distance measure based on the representation emerging from the ordinal factorization to discover similar items. To evaluate the method, we conduct a case study on different datasets.
The growing energy and performance costs of deep learning have driven the community to reduce the size of neural networks by selectively pruning components. Similarly to their biological counterparts, sparse networks generalize just as well, if not better than, the original dense networks. Sparsity can reduce the memory footprint of regular networks to fit mobile devices, as well as shorten training time for ever growing networks. In this paper, we survey prior work on sparsity in deep learning and provide an extensive tutorial of sparsification for both inference and training. We describe approaches to remove and add elements of neural networks, different training strategies to achieve model sparsity, and mechanisms to exploit sparsity in practice. Our work distills ideas from more than 300 research papers and provides guidance to practitioners who wish to utilize sparsity today, as well as to researchers whose goal is to push the frontier forward. We include the necessary background on mathematical methods in sparsification, describe phenomena such as early structure adaptation, the intricate relations between sparsity and the training process, and show techniques for achieving acceleration on real hardware. We also define a metric of pruned parameter efficiency that could serve as a baseline for comparison of different sparse networks. We close by speculating on how sparsity can improve future workloads and outline major open problems in the field.
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