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The multinomial logistic regression (MLR) model is widely used in statistics and machine learning. Stochastic gradient descent (SGD) is the most common approach for determining the parameters of a MLR model in big data scenarios. However,…

In this paper, we investigate federated learning for quantile inference under local differential privacy (LDP). We propose an estimator based on local stochastic gradient descent (SGD), whose local gradients are perturbed via a randomized…

Infinitesimal contraction analysis provides exponential convergence rates between arbitrary pairs of trajectories of a system by studying the system's linearization. An essentially equivalent viewpoint arises through stability analysis of a…

Using the ratios conjectures as introduced by Conrey, Farmer and Zirnbauer, we obtain closed formulas for the one-level density for two families of L-functions attached to elliptic curves. From those closed formulas, we can determine the…

The family of symmetric powers of an $L$-function associated with an elliptic curve with complex multiplication has received much attention from algebraic, automorphic and p-adic points of view. Here we examine one explicit such family from…

Stochastic Gradient Descent (SGD) is widely used in machine learning research. Previous convergence analyses of SGD under the vanishing step-size setting typically require Robbins-Monro conditions. However, in practice, a wider variety of…

We consider Bayesian multiple statistical classification problem in the case where the unknown source distributions are estimated from the labeled training sequences, then the estimates are used as nominal distributions in a robust…

The concept of statistical convergence based on asymptotic density is introduced in this article through nets. Some possible extensions of classical results for statistical convergence of sequences are obtained in this article, with…

We propose the supervised hierarchical Dirichlet process (sHDP), a nonparametric generative model for the joint distribution of a group of observations and a response variable directly associated with that whole group. We compare the sHDP…

Appropriately evaluating the discrepancy between domains is essential for the success of unsupervised domain adaptation. In this paper, we first point out that existing discrepancy measures are less informative when complex models such as…

Likelihood-free inference for simulator-based statistical models has recently attracted a surge of interest, both in the machine learning and statistics communities. The primary focus of these research fields has been to approximate the…

Aligning Large Language Models (LLMs) is crucial for enhancing their safety and utility. However, existing methods, primarily based on preference datasets, face challenges such as noisy labels, high annotation costs, and privacy concerns.…

We use a Mellin-Barnes integral representation for the Lerch transcendent $\Phi(z,s,a)$ to obtain large $z$ asymptotic approximations. The simplest divergent asymptotic approximation terminates in the case that $s$ is an integer. For…

In real-world regression tasks, datasets frequently exhibit imbalanced distributions, characterized by a scarcity of data in high-complexity regions and an abundance in low-complexity areas. This imbalance presents significant challenges…

The theory of summability of divergent series is a major branch of mathematical analysis that has found important applications in engineering and science. It addresses methods of assigning natural values to divergent sums, whose…

Probabilistic Logic Programs (PLPs) generalize traditional logic programs and allow the encoding of models combining logical structure and uncertainty. In PLP, inference is performed by summarizing the possible worlds which entail the query…

Statistical inference problems arising within signal processing, data mining, and machine learning naturally give rise to hard combinatorial optimization problems. These problems become intractable when the dimensionality of the data is…

Datasets from the fields of bioinformatics, chemometrics, and face recognition are typically characterized by small samples of high-dimensional data. Among the many variants of linear discriminant analysis that have been proposed in order…

Delattre et al. (2013) considered n independent stochastic differential equations (SDEs), where in each case the drift term is associated with a random effect, the distribution of which depends upon unknown parameters. Assuming the…

The focus of this work is on Statistical Process Control (SPC) of a manufacturing process based on available measurements. Two important applications of SPC in industrial settings are fault detection and diagnosis (FDD). In this work a deep…