Related papers: Distribution-Independent Regression for Generalize…

There has been a growing interest in using non-parametric regression methods like Gaussian Process (GP) regression for system identification. GP regression does traditionally have three important downsides: (1) it is computationally…

The paper introduces a novel methodology for the identification of coefficients of switched autoregressive linear models. We consider the case when the system's outputs are contaminated by possibly large values of measurement noise. It is…

Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…

Generalized linear model or GLM constitutes a large class of models and essentially extends the ordinary linear regression by connecting the mean of the response variable with the covariate through appropriate link functions. On the other…

Current state-of-the-art deep learning systems for visual object recognition and detection use purely supervised training with regularization such as dropout to avoid overfitting. The performance depends critically on the amount of labeled…

In real-world datasets, noisy labels are pervasive. The challenge of learning with noisy labels (LNL) is to train a classifier that discerns the actual classes from given instances. For this, the model must identify features indicative of…

Generalized linear models (GLMs) -- such as logistic regression, Poisson regression, and robust regression -- provide interpretable models for diverse data types. Probabilistic approaches, particularly Bayesian ones, allow coherent…

Unmeasured or latent variables are often the cause of correlations between multivariate measurements, which are studied in a variety of fields such as psychology, ecology, and medicine. For Gaussian measurements, there are classical tools…

Learning with Noisy Labels (LNL) has attracted significant attention from the research community. Many recent LNL methods rely on the assumption that clean samples tend to have "small loss". However, this assumption always fails to…

The autoregressive time series model is a popular second-order stationary process, modeling a wide range of real phenomena. However, in applications, autoregressive signals are often corrupted by additive noise. Further, the autoregressive…

This paper develops asymptotic theory for estimation of parameters in regression models for binomial response time series where serial dependence is present through a latent process. Use of generalized linear model (GLM) estimating…

Label noise and class imbalance are two major issues coexisting in real-world datasets. To alleviate the two issues, state-of-the-art methods reweight each instance by leveraging a small amount of clean and unbiased data. Yet, these methods…

A linear structural equation model relates random variables of interest and corresponding Gaussian noise terms via a linear equation system. Each such model can be represented by a mixed graph in which directed edges encode the linear…

Diffusion models have become a leading paradigm in generative AI, with score estimation via denoising score matching as a central component. While recent theory provides strong statistical guarantees, it typically relies on…

We consider a sparse high dimensional regression model where the goal is to recover a $k$-sparse unknown vector $\beta^*$ from $n$ noisy linear observations of the form $Y=X\beta^*+W \in \mathbb{R}^n$ where $X \in \mathbb{R}^{n \times p}$…

This paper is centered around the approximation of dynamical systems by means of Gaussian processes. To this end, trajectories of such systems must be collected to be used as training data. The measurements of these trajectories are…

Gamma hadron classification, a central machine learning task in gamma ray astronomy, is conventionally tackled with supervised learning. However, the supervised approach requires annotated training data to be produced in sophisticated and…

Suppose that we observe $y \in \mathbb{R}^f$ and $X \in \mathbb{R}^{f \times m}$ in the following errors-in-variables model: \begin{eqnarray*} y & = & X_0 \beta^* + \epsilon \\ X & = & X_0 + W \end{eqnarray*} where $X_0$ is a $f \times m$…

Graph Neural Networks (GNNs) have achieved promising results for semi-supervised learning tasks on graphs such as node classification. Despite the great success of GNNs, many real-world graphs are often sparsely and noisily labeled, which…

Gaussian Process (GP) regression models typically assume that residuals are Gaussian and have the same variance for all observations. However, applications with input-dependent noise (heteroscedastic residuals) frequently arise in practice,…