Related papers: Convergence rate for predictive recursion estimati…

In this work, we provide a fundamental unified convergence theorem used for deriving expected and almost sure convergence results for a series of stochastic optimization methods. Our unified theorem only requires to verify several…

This paper introduces a new approach to the study of rates of convergence for posterior distributions. It is a natural extension of a recent approach to the study of Bayesian consistency. In particular, we improve on current rates of…

The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…

In this paper, we focus on the problem of conformal prediction with conditional guarantees. Prior work has shown that it is impossible to construct nontrivial prediction sets with full conditional coverage guarantees. A wealth of research…

Penalties that induce smoothness are common in nonparametric regression. In many settings, the amount of smoothness in the data generating function will not be known. Simon and Shojaie (2021) derived convergence rates for nonparametric…

When machine learning systems meet real world applications, accuracy is only one of several requirements. In this paper, we assay a complementary perspective originating from the increasing availability of pre-trained and regularly…

Finite mixture models are widely used in econometric analyses to capture unobserved heterogeneity. This paper shows that maximum likelihood estimation of finite mixtures of parametric densities can suffer from substantial finite-sample bias…

Accurate probabilistic predictions can be characterized by two properties -- calibration and sharpness. However, standard maximum likelihood training yields models that are poorly calibrated and thus inaccurate -- a 90% confidence interval…

Motivated by the desire to understand stochastic algorithms for nonconvex optimization that are robust to their hyperparameter choices, we analyze a mini-batched prox-linear iterative algorithm for the problem of recovering an unknown…

This paper proposes a novel discriminative regression method, called adaptive locality preserving regression (ALPR) for classification. In particular, ALPR aims to learn a more flexible and discriminative projection that not only preserves…

Consider the problem of joint parameter estimation and prediction in a Markov random field: i.e., the model parameters are estimated on the basis of an initial set of data, and then the fitted model is used to perform prediction (e.g.,…

When randomized ensembles such as bagging or random forests are used for binary classification, the prediction error of the ensemble tends to decrease and stabilize as the number of classifiers increases. However, the precise relationship…

Mixtures of linear mixed models (MLMMs) are useful for clustering grouped data and can be estimated by likelihood maximization through the EM algorithm. The conventional approach to determining a suitable number of components is to compare…

Trajectory prediction is critical for autonomous driving, enabling safe and efficient planning in dense, dynamic traffic. Most existing methods optimize prediction accuracy under fixed-length observations. However, real-world driving often…

We present a deep transformation model for probabilistic regression. Deep learning is known for outstandingly accurate predictions on complex data but in regression tasks, it is predominantly used to just predict a single number. This…

Computing the rate-distortion function for continuous sources is commonly regarded as a standard continuous optimization problem. When numerically addressing this problem, a typical approach involves discretizing the source space and…

Exact inference in the linear regression model with spike and slab priors is often intractable. Expectation propagation (EP) can be used for approximate inference. However, the regular sequential form of EP (R-EP) may fail to converge in…

Modern applications require methods that are computationally feasible on large datasets but also preserve statistical efficiency. Frequently, these two concerns are seen as contradictory: approximation methods that enable computation are…

The convergence of expectation-maximization (EM)-based algorithms typically requires continuity of the likelihood function with respect to all the unknown parameters (optimization variables). The requirement is not met when parameters…

Conformal prediction constructs a confidence set for an unobserved response of a feature vector based on previous identically distributed and exchangeable observations of responses and features. It has a coverage guarantee at any nominal…