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While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy…
This paper proposes a fast and accurate method for sparse regression in the presence of missing data. The underlying statistical model encapsulates the low-dimensional structure of the incomplete data matrix and the sparsity of the…
High-dimensional data analysis has been an active area, and the main focuses have been variable selection and dimension reduction. In practice, it occurs often that the variables are located on an unknown, lower-dimensional nonlinear…
We introduce generative models for accelerating simulations of complex systems through learning and evolving their effective dynamics. In the proposed Generative Learning of Effective Dynamics (G-LED), instances of high dimensional data are…
Imitation Learning (IL) is an appealing approach to learn desirable autonomous behavior. However, directing IL to achieve arbitrary goals is difficult. In contrast, planning-based algorithms use dynamics models and reward functions to…
This paper considers the problem of learning a single ReLU neuron with squared loss (a.k.a., ReLU regression) in the overparameterized regime, where the input dimension can exceed the number of samples. We analyze a Perceptron-type…
Selective inference aims at providing valid inference after a data-driven selection of models or hypotheses. It is essential to avoid overconfident results and replicability issues. While significant advances have been made in this area for…
We propose a general framework for non-normal multivariate data analysis called multivariate covariance generalized linear models (McGLMs), designed to handle multivariate response variables, along with a wide range of temporal and spatial…
Linear regression is a fundamental modeling tool in statistics and related fields. In this paper, we study an important variant of linear regression in which the predictor-response pairs are partially mismatched. We use an optimization…
The problem of learning single index and multi index models has gained significant interest as a fundamental task in high-dimensional statistics. Many recent works have analysed gradient-based methods, particularly in the setting of…
The linear model uses the space defined by the input to project the target or desired signal and find the optimal set of model parameters. When the problem is nonlinear, the adaption requires nonlinear models for good performance, but it…
Recently, many machine learning and statistical models such as non-linear regressions, the Single Index, Multi-index, Varying Coefficient Index Models and Two-layer Neural Networks can be reduced to or be seen as a special case of a new…
Autoregressive models (ARMs) currently hold state-of-the-art performance in likelihood-based modeling of image and audio data. Generally, neural network based ARMs are designed to allow fast inference, but sampling from these models is…
Although graph neural networks (GNNs) have made great progress recently on learning from graph-structured data in practice, their theoretical guarantee on generalizability remains elusive in the literature. In this paper, we provide a…
Learning general latent-variable probabilistic graphical models is a key theoretical challenge in machine learning and artificial intelligence. All previous methods, including the EM algorithm and the spectral algorithms, face severe…
Estimation in generalized linear models (GLM) is complicated by the presence of constraints. One can handle constraints by maximizing a penalized log-likelihood. Penalties such as the lasso are effective in high dimensions, but often lead…
Spatiotemporal data consisting of timestamps, GPS coordinates, and IDs occurs in many settings. Modeling approaches for this type of data must address challenges in terms of sensor noise, uneven sampling rates, and non-persistent IDs. In…
Linear time-invariant systems are very popular models in system theory and applications. A fundamental problem in system identification that remains rather unaddressed in extant literature is to leverage commonalities amongst related linear…
Growth curve models are popular tools for studying the development of a response variable within subjects over time. Heterogeneity between subjects is common in such models, and researchers are typically interested in explaining or…
High-dimensional datasets are frequently subject to contamination by outliers and heavy-tailed noise, which can severely bias standard regularized estimators like the Lasso. While Maximum Mean Discrepancy (MMD) has recently been introduced…