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In this work, we investigate data fitting problems with random noises. A randomized progressive iterative regularization method is proposed. It works well for large-scale matrix computations and converges in expectation to the least-squares…
Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the…
In this paper, we propose a new Bayesian inference method for a high-dimensional sparse factor model that allows both the factor dimensionality and the sparse structure of the loading matrix to be inferred. The novelty is to introduce a…
Supervised machine learning models often associate irrelevant nuisance factors with the prediction target, which hurts generalization. We propose a framework for training robust neural networks that induces invariance to nuisances through…
We propose a new estimator of high-dimensional spot volatility matrices satisfying a low-rank plus sparse structure from noisy and asynchronous high-frequency data collected for an ultra-large number of assets. The noise processes are…
Reliability analysis aims at estimating the failure probability of an engineering system. It often requires multiple runs of a limit-state function, which usually relies on computationally intensive simulations. Traditionally, these…
In label-noise learning, estimating the transition matrix has attracted more and more attention as the matrix plays an important role in building statistically consistent classifiers. However, it is very challenging to estimate the…
The ever-increasing parameter counts of deep learning models necessitate effective compression techniques for deployment on resource-constrained devices. This paper explores the application of information geometry, the study of…
From CNNs to attention mechanisms, encoding inductive biases into neural networks has been a fruitful source of improvement in machine learning. Adding auxiliary losses to the main objective function is a general way of encoding biases that…
Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…
Model-based methods and deep neural networks have both been tremendously successful paradigms in machine learning. In model-based methods, problem domain knowledge can be built into the constraints of the model, typically at the expense of…
We address the problem of estimating a sparse low-rank matrix from its noisy observation. We propose an objective function consisting of a data-fidelity term and two parameterized non-convex penalty functions. Further, we show how to set…
Collecting large-scale datasets is crucial for training deep models, annotating the data, however, inevitably yields noisy labels, which poses challenges to deep learning algorithms. Previous efforts tend to mitigate this problem via…
Factorizing a large matrix into small matrices is a popular strategy for model compression. Singular value decomposition (SVD) plays a vital role in this compression strategy, approximating a learned matrix with fewer parameters. However,…
Deep learning provides accurate collaborative filtering models to improve recommender system results. Deep matrix factorization and their related collaborative neural networks are the state-of-art in the field; nevertheless, both models…
We propose a method for noise reduction, the task of producing a clean audio signal from a recording corrupted by additive noise. Many common approaches to this problem are based upon applying non-negative matrix factorization to…
A key element in transfer learning is representation learning; if representations can be developed that expose the relevant factors underlying the data, then new tasks and domains can be learned readily based on mappings of these salient…
Boolean matrix factorization and Boolean matrix completion from noisy observations are desirable unsupervised data-analysis methods due to their interpretability, but hard to perform due to their NP-hardness. We treat these problems as…
This paper examines fundamental error characteristics for a general class of matrix completion problems, where the matrix of interest is a product of two a priori unknown matrices, one of which is sparse, and the observations are noisy. Our…
Diffusion models are a popular class of generative models trained to reverse a noising process starting from a target data distribution. Training a diffusion model consists of learning how to denoise noisy samples at different noise levels.…