相关论文: The Conditional Cauchy-Schwarz Divergence with App…

We construct and study a time--semidiscretization scheme for the Cauchy problem associated with a linear homogeneous differential equation with the Caputo fractional time derivative of order $\alpha\in(0,1)$ and a spatial sectorial operator…

\cite{tsagris2025a} proposed the generalized circular projected Cauchy (GCPC) distribution, whose special case is the wrapped Cauchy distribution. In this paper we first derive the relationship with the wrapped Cauchy distribution, and then…

We introduce computational causal inference as an interdisciplinary field across causal inference, algorithms design and numerical computing. The field aims to develop software specializing in causal inference that can analyze massive…

We study the problem of closeness testing for continuous distributions and its implications for causal discovery. Specifically, we analyze the sample complexity of distinguishing whether two multidimensional continuous distributions are…

Sequential hypothesis testing is a desirable decision making strategy in any time sensitive scenario. Compared with fixed sample-size testing, sequential testing is capable of achieving identical probability of error requirements using less…

We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution $P_{Y \mid X}$. Existing methods, such as conformalized quantile regression and…

We prove a general inequality for more than two sequences mirroring that of the discrete two-sequence Cauchy-Schwarz.

Beneficial to advanced computing devices, models with massive parameters are increasingly employed to extract more information to enhance the precision in describing and predicting the patterns of objective systems. This phenomenon is…

In this paper, we study the possibility of designing non-trivial random CSP models by exploiting the intrinsic connection between structures and typical-case hardness. We show that constraint consistency, a notion that has been developed to…

Uncertainty is critical to reliable decision-making with machine learning. Conformal prediction (CP) handles uncertainty by predicting a set on a test input, hoping the set to cover the true label with at least $(1-\alpha)$ confidence. This…

Modern black-box predictive models are often accompanied by weak performance guarantees that only hold asymptotically in the size of the dataset or require strong parametric assumptions. In response to this, split conformal prediction…

Recent advances in Bayesian models for random partitions have led to the formulation and exploration of Exchangeable Sequences of Clusters (ESC) models. Under ESC models, it is the cluster sizes that are exchangeable, rather than the…

We consider a class of stochastic optimal control problems with partial observation, and study their approximation by discrete-time control problems. We establish a convergence result by using weak convergence technique of Kushner and…

The strong convergence of Euler approximations of stochastic delay differential equations is proved under general conditions. The assumptions on drift and diffusion coefficients have been relaxed to include polynomial growth and only…

Chance constrained programming (CCP) refers to a type of optimization problem with uncertain constraints that are satisfied with at least a prescribed probability level. In this work, we study the sample average approximation (SAA) of…

Causal discovery studies the problem of mining causal relationships between variables from data, which is of primary interest in science. During the past decades, significant amount of progresses have been made toward this fundamental data…

Time series similarity measures are highly relevant in a wide range of emerging applications including training machine learning models, classification, and predictive modeling. Standard similarity measures for time series most often…

Accurate conditional prediction in the regression setting plays an important role in many real-world problems. Typically, a point prediction often falls short since no attempt is made to quantify the prediction accuracy. Classically, under…

We establish rates of convergences in time series forecasting using the statistical learning approach based on oracle inequalities. A series of papers extends the oracle inequalities obtained for iid observations to time series under weak…

Spectral Clustering(SC) is a prominent data clustering technique of recent times which has attracted much attention from researchers. It is a highly data-driven method and makes no strict assumptions on the structure of the data to be…