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Given p independent normal populations, we consider the problem of estimating the mean of those populations, that based on the observed data, give the strongest signals. We explicitly condition on the ranking of the sample means, and…

Probabilistic graphical models are a key tool in machine learning applications. Computing the partition function, i.e., normalizing constant, is a fundamental task of statistical inference but it is generally computationally intractable,…

Efficient sampling from the Boltzmann distribution given its energy function is a key challenge for modeling complex physical systems such as molecules. Boltzmann Generators address this problem by leveraging continuous normalizing flows to…

With the rapid advancement of large language models , code generation has become a key benchmark for evaluating LLM capabilities. However, existing benchmarks face two major challenges: (1) the escalating cost of constructing high-quality…

The success of any machine learning system depends critically on effective representations of data. In many cases, it is desirable that a representation scheme uncovers the parts-based, additive nature of the data. Of current representation…

Estimating a Gibbs density function given a sample is an important problem in computational statistics and statistical learning. Although the well established maximum likelihood method is commonly used, it requires the computation of the…

We present some new density estimation algorithms obtained by bootstrap aggregation like Bagging. Our algorithms are analyzed and empirically compared to other methods found in the statistical literature, like stacking and boosting for…

Interest in Restricted Boltzmann Machine (RBM) is growing as a generative stochastic artificial neural network to implement a novel energy-efficient machine-learning (ML) technique. For a hardware implementation of the RBM, an essential…

We propose in this work RBM-SVGD, a stochastic version of Stein Variational Gradient Descent (SVGD) method for efficiently sampling from a given probability measure and thus useful for Bayesian inference. The method is to apply the Random…

Maximum likelihood estimators are proposed for the parameters and the densities in a semiparametric density ratio model in which the nonparametric baseline density is approximated by the Bernstein polynomial model. The EM algorithm is used…

The restricted Boltzmann machine (RBM) is a flexible tool for modeling complex data, however there have been significant computational difficulties in using RBMs to model high-dimensional multinomial observations. In natural language…

Relative error estimation has been recently used in regression analysis. A crucial issue of the existing relative error estimation procedures is that they are sensitive to outliers. To address this issue, we employ the $\gamma$-likelihood…

Restricted Boltzmann machines~(RBMs) and conditional RBMs~(CRBMs) are popular models for a wide range of applications. In previous work, learning on such models has been dominated by contrastive divergence~(CD) and its variants. Belief…

Large-scale electrophysiological recordings now allow simultaneous monitoring of thousands of neurons across multiple brain regions, revealing structured variability in neural population activity. Understanding how these collective patterns…

Recent advances in deep learning and neural networks have led to an increased interest in the application of generative models in statistical and condensed matter physics. In particular, restricted Boltzmann machines (RBMs) and variational…

Driven by applications in telecommunication networks, we explore the simulation task of estimating rare event probabilities for tandem queues in their steady state. Existing literature has recognized that importance sampling methods can be…

An important way to make large training sets is to gather noisy labels from crowds of non experts. We propose a method to aggregate noisy labels collected from a crowd of workers or annotators. Eliciting labels is important in tasks such as…

The Restricted Boltzmann Machine (RBM), an important tool used in machine learning in particular for unsupervized learning tasks, is investigated from the perspective of its spectral properties. Starting from empirical observations, we…

Expectation-Maximization (EM) algorithm is a widely used iterative algorithm for computing maximum likelihood estimate when dealing with Gaussian Mixture Model (GMM). When the sample size is smaller than the data dimension, this could lead…

Advanced classification algorithms are being increasingly used in safety-critical applications like health-care, engineering, etc. In such applications, miss-classifications made by ML algorithms can result in substantial financial or…