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Regression trees are a popular machine learning algorithm that fit piecewise constant models by recursively partitioning the predictor space. This paper focuses on statistical inference for a data-dependent model obtained from a fitted…
Parametric stochastic simulators are ubiquitous in science, often featuring high-dimensional input parameters and/or an intractable likelihood. Performing Bayesian parameter inference in this context can be challenging. We present a neural…
The reduced-rank regression model is a popular model to deal with multivariate response and multiple predictors, and is widely used in biology, chemometrics, econometrics, engineering, and other fields. In the reduced-rank regression…
Representation based classification methods have become a hot research topic during the past few years, and the two most prominent approaches are sparse representation based classification (SRC) and collaborative representation based…
Parameter estimation for the truncated skew-normal distribution is challenging, as truncation introduces additional nonlinearity into the likelihood function and often leads to numerical instability in existing estimation procedures. In…
Sparse representation-based classification (SRC), proposed by Wright et al., seeks the sparsest decomposition of a test sample over the dictionary of training samples, with classification to the most-contributing class. Because it assumes…
Reduced rank regression (RRR) is a statistical method for finding a low-dimensional linear mapping between a set of high-dimensional inputs and outputs. In recent years, RRR has found numerous applications in neuroscience, in particular for…
This paper introduces a practical sampling method for training surrogate models in the context of uncertainty propagation. We propose a heuristic method to uniformly draw samples within highest density regions of the density given by the…
Reduced-rank (RR) regression may be interpreted as a dimensionality reduction technique able to reveal complex relationships among the data parsimoniously. However, RR regression models typically overlook any potential group structure among…
Seeking to improve model generalization, we consider a new approach based on distributionally robust learning (DRL) that applies stochastic gradient descent to the outer minimization problem. Our algorithm efficiently estimates the gradient…
The distribution of seismic moment is of capital interest to evaluate earthquake hazard, in particular regarding the most extreme events. We make use of likelihood-ratio tests to compare the simple Gutenberg-Richter power-law distribution…
We introduce a class of regularized M-estimators of multivariate scatter and show, analogous to the popular spatial sign covariance matrix (SSCM), that they possess high breakdown points. We also show that the SSCM can be viewed as an…
This paper introduces a framework for Chance-Constrained Optimization with Complex Variables, addressing complex linear programming for both individual and joint probabilistic constraints in the complex domain. We first analyze the 3CP…
The measurement error with normal distribution is universal in applications. Generally, smaller measurement error requires better instrument and higher test cost. In decision making based on attribute values of objects, we shall select an…
Training models that perform well under distribution shifts is a central challenge in machine learning. In this paper, we introduce a modeling framework where, in addition to training data, we have partial structural knowledge of the…
Currently the most popular method of providing robustness certificates is randomized smoothing where an input is smoothed via some probability distribution. We propose a novel approach to randomized smoothing over multiplicative parameters.…
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…
Input variables in numerical models are often subject to several levels of uncertainty, usually modeled by probability distributions. In the context of uncertainty quantification applied to these models, studying the robustness of output…
The RRUM is a model that is frequently seen in language assessment studies. The objective of this research is to advance an MCMC algorithm for the Bayesian RRUM. The algorithm starts with estimating correlated attributes. Using a saturated…
To improve the utility and scalability of distributed radio frequency (RF) sensor and communication networks, reduce the need for convolutional neural network (CNN) retraining, and efficiently share learned information about signals, we…