机器学习

In this article, we study the problem of sampling from distributions whose densities are not necessarily smooth nor logconcave. We propose a simple Langevin-based algorithm that does not rely on popular but computationally challenging…

Forecast reconciliation is considered an effective method to achieve coherence (within a forecast hierarchy) and to improve forecast quality. However, the value of reconciled forecasts in downstream decision-making tasks has been mostly…

We consider Heterogeneous Transfer Learning (HTL) from a source to a new target domain for high-dimensional regression with differing feature sets. Most homogeneous TL methods assume that target and source domains share the same feature…

Model selection is the process of choosing from a class of candidate models given data. For instance, methods such as the LASSO and sparse identification of nonlinear dynamics (SINDy) formulate model selection as finding a sparse solution…

We study the problem of post-selection predictive inference in an online fashion. To avoid devoting resources to unimportant units, a preliminary selection of the current individual before reporting its prediction interval is common and…

This report investigates the fitting of the Hessian or its inverse for stochastic optimizations using a Hessian fitting criterion derived from the preconditioned stochastic gradient descent (PSGD) method. This criterion is closely related…

Quantile Regression Forests (QRF) are widely used for non-parametric conditional quantile estimation, yet statistical inference for variable importance measures remains challenging due to the non-smoothness of the loss function and the…

In traditional multivariate data analysis, dimension reduction and regression have been treated as distinct endeavors. Established techniques such as principal component regression (PCR) and partial least squares (PLS) regression…

Bayesian computational strategies for inference can be inefficient in approximating the posterior distribution in models that exhibit some form of periodicity. This is because the probability mass of the marginal posterior distribution of…

Selecting the best alternative from a finite set represents a broad class of pure exploration problems. Traditional approaches to pure exploration have predominantly relied on Gaussian or sub-Gaussian assumptions on the performance…

Support vector machines are widely used in machine learning classification tasks, but traditional SVM models suffer from sensitivity to outliers and instability in resampling, which limits their performance in practical applications. To…

Uncertainty quantification is vital for decision-making and risk assessment in machine learning. Mean-variance regression models, which predict both a mean and residual noise for each data point, provide a simple approach to uncertainty…

Most scientific domains elicit the development of efficient algorithms and accessible scientific software. This thesis unifies our developments in three broad domains: Quasi-Monte Carlo (QMC) methods for efficient high-dimensional…

The abundance of fine-grained spatio-temporal data, such as traffic sensor networks, offers vast opportunities for scientific discovery. However, inferring causal relationships from such observational data remains challenging, particularly…

Property elicitation studies which attributes of a probability distribution can be determined by minimizing a risk. We investigate a generalization of property elicitation to imprecise probabilities (IP). This investigation is motivated by…

In real-world applications, anomaly detection (AD) often operates without access to anomalous data, necessitating semi-supervised methods that rely solely on normal data. Among these methods, deep k-nearest neighbor (deep kNN) AD stands out…

Conformal prediction is a non-parametric technique for constructing prediction intervals or sets from arbitrary predictive models under the assumption that the data is exchangeable. It is popular as it comes with theoretical guarantees on…

Analyzing neural network dynamics via stochastic gradient descent (SGD) is crucial to building theoretical foundations for deep learning. Previous work has analyzed structured inputs within the \textit{hidden manifold model}, often under…

Causal effect estimation in networked systems is central to data-driven decision making. In such settings, interventions on one unit can spill over to others, and in complex physical or social systems, the interaction pathways driving these…

A fundamental theoretical question in network analysis is to determine under which conditions community recovery is possible in polynomial time in the Stochastic Block Model (SBM). When the number $K$ of communities remains smaller than…