Statistics
Identifying the causal effects of socioeconomic determinants on population health is of many great interests - from statistical methodology development to public health practitioners and policy developments. The statistical side of the…
Constrained sampling is an important and challenging task in computational statistics, concerned with generating samples from a distribution under certain constraints. There are numerous types of algorithm aimed at this task, ranging from…
Forecasting accuracy is bounded by the information available about the future. This paper makes that statement precise using information-theoretic tools. Under logarithmic loss, the expected performance of any probabilistic forecast…
This thesis presents Regenerative Rejection Sampling (RRS), a novel approximate sampling algorithm inspired by classical Rejection Sampling and Markov Chain Monte Carlo methods. The method constructs a continuous-time regenerative process…
We consider the discrete-time filtering problem in scenarios where the observation noise is low or degenerate. We focus on the case where the observation equation is a linear function of the state and the data involve additive noise.…
Accurate day-ahead electricity price forecasts are critical for power system operation and market participation, yet growing renewable penetration and recent crises have caused unprecedented volatility that challenges standard models. This…
This paper addresses the nonparametric estimation of the drift function over a compact domain for a time-homogeneous diffusion process, based on high-frequency discrete observations from $N$ independent trajectories. We propose a neural…
Causal discovery methods can identify valid adjustment sets for causal effect estimation for a pair of target variables, even when the underlying causal graph is unknown. Global causal discovery methods focus on learning the whole causal…
Spatial fields in the Earth and environmental sciences are often available at multiple scales or resolutions. While coarse-scale data (e.g., from global circulation models) are often abundant, they lack the local detail provided by…
Recent advances in large language model (LLM) embeddings have enabled powerful representations for biological data, but most applications to date focus on gene-level information. We present one of the first systematic frameworks to generate…
Shampoo and its efficient variant, SOAP, employ structured second-moment estimations and have shown strong performance for training neural networks (NNs). In practice, however, Shampoo typically requires step-size grafting with Adam to be…
Bayesian Additive Regression Trees (BART) is a powerful statistical model that leverages the strengths of Bayesian inference and regression trees. It has received significant attention for capturing complex non-linear relationships and…
Higher-order $U$-statistics abound in fields such as statistics, machine learning, and computer science, but are known to be highly time-consuming to compute in practice. Despite their widespread appearance, a comprehensive study of their…
The identification of Linear Time-Varying (LTV) systems from input-output data is a fundamental yet challenging ill-posed inverse problem. This work introduces a unified Bayesian framework that models the system's impulse response, $h(t,…
Tree ensembles are non-parametric methods widely recognized for their accuracy and ability to capture complex interactions. While these models excel at prediction, they are difficult to interpret and may fail to uncover useful relationships…
Computer Adaptive Testing (CAT) aims to accurately estimate an individual's ability using only a subset of an Item Response Theory (IRT) instrument. Many applications also require diverse item exposure across testing sessions, preventing…
The tetrad constraint is widely used to test whether four observed variables are conditionally independent given a latent variable, based on the fact that if four observed variables following a linear model are mutually independent after…
Instrumental variable methods are widely used for causal inference, but identification becomes especially challenging when instruments are weak and potentially invalid. These challenges are particularly pronounced in Mendelian…
Gaussian Processes (GPs) provide a flexible and statistically principled foundation for modelling spatiotemporal phenomena, but their $O(N^3)$ scaling makes them intractable for large datasets. Approximate methods such as variational…
Controlling the false discovery rate (FDR) is a critical challenge in large-scale data analysis, particularly in the presence of outliers. A common practice involves imposing a Student-$t$ distribution to eliminate the influence of…