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Density level sets can be estimated using plug-in methods, excess mass algorithms or a hybrid of the two previous methodologies. The plug-in algorithms are based on replacing the unknown density by some nonparametric estimator, usually the…

This paper proposes a sparse regression strategy for discovery of ordinary differential equations from incomplete and noisy data. Inference is performed over both equation parameters and state variables using a statistically motivated…

Structural learning, a method to estimate the parameters for discrete energy minimization, has been proven to be effective in solving computer vision problems, especially in 3D scene parsing. As the complexity of the models increases,…

Variational inference using the reparameterization trick has enabled large-scale approximate Bayesian inference in complex probabilistic models, leveraging stochastic optimization to sidestep intractable expectations. The reparameterization…

In this paper we propose a solution to the problem of parameter estimation of nonlinearly parameterized regressions--continuous or discrete time--and apply it for system identification and adaptive control. We restrict our attention to…

This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery…

In this paper we describe a new method for detecting and counting a repeating object in an image. While the method relies on a fairly sophisticated deformable part model, unlike existing techniques it estimates the model parameters in an…

The advent of advanced crystallographic techniques has shifted structural biology from static, single-conformer models toward probing protein dynamics. Extracting cooperative motions from temporally and spatially averaged electron density…

Kernel density estimation is a popular method for estimating unseen probability distributions. However, the convergence of these classical estimators to the true density slows down in high dimensions. Moreover, they do not define meaningful…

Model averaging has demonstrated superior performance for ensemble forecasting in high-dimensional framework, its extension to incomplete datasets remains a critical but underexplored challenge. Moreover, identifying the parsimonious model…

Probabilistic Regression refers to predicting a full probability density function for the target conditional on the features. We present a nonparametric approach to this problem which combines base classifiers (typically gradient boosted…

Density ratio estimation (DRE) is a paramount task in machine learning, for its broad applications across multiple domains, such as covariate shift adaptation, causal inference, independence tests and beyond. Parametric methods for…

Probability density estimation is a core problem of statistics and signal processing. Moment methods are an important means of density estimation, but they are generally strongly dependent on the choice of feasible functions, which severely…

With promising empirical performance across a wide range of applications, synthetic data augmentation appears a viable solution to data scarcity and the demands of increasingly data-intensive models. Its effectiveness lies in expanding the…

Attrition in survey and field experiments presents a challenge for social science research. Common approaches to deal with this problem -- such as complete case analysis, multiple imputation, and weighting methods -- rely on strong…

Dealing with distribution shifts is one of the central challenges for modern machine learning. One fundamental situation is the covariate shift, where the input distributions of data change from training to testing stages while the…

Modern statistical inference tasks often require iterative optimization methods to compute the solution. Convergence analysis from an optimization viewpoint only informs us how well the solution is approximated numerically but overlooks the…

Predictive recursion (PR) is a fast algorithm for nonparametric estimation of a mixing density, with connections to sequential Bayesian updating under a Dirichlet process prior and rigorous frequentist consistency guarantees. Extending PR…

This paper presents a new parameter estimation algorithm for the adaptive control of a class of time-varying plants. The main feature of this algorithm is a matrix of time-varying learning rates, which enables parameter estimation error…

Iterative refinement -- start with a random guess, then iteratively improve the guess -- is a useful paradigm for representation learning because it offers a way to break symmetries among equally plausible explanations for the data. This…