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Local Polynomial Regression (LPR) is a powerful tool for nonparametric smoothing, yet it traditionally suffers from a "Euclidean tautology": the variables used to define the local neighborhood are identical to those used in the polynomial…
Generalized causal effect estimands, including the Mann-Whitney parameter and causal net benefit, provide flexible summaries of treatment effects in randomized experiments with non-Gaussian or multivariate outcomes. We develop a unified…
The mining and exploitation of graph structural information have been the focal points in the study of complex networks. Traditional structural measures in Network Science focus on the analysis and modelling of complex networks from the…
Recently, there has been a growing interest for mixed-categorical meta-models based on Gaussian process (GP) surrogates. In this setting, several existing approaches use different strategies either by using continuous kernels (e.g.,…
The class of Generalized $L$-statistics ($GL$-statistics) unifies a broad class of different estimators, for example scale estimators based on multivariate kernels. $GL$-statistics are functionals of $U$-quantiles and therefore the…
This PhD thesis contains several contributions to the field of statistical causal modeling. Statistical causal models are statistical models embedded with causal assumptions that allow for the inference and reasoning about the behavior of…
Quantitative analysis of large-scale data is often complicated by the presence of diverse subgroups, which reduce the accuracy of inferences they make on held-out data. To address the challenge of heterogeneous data analysis, we introduce…
This paper presents and analyzes an approach to cluster-based inference for dependent data. The primary setting considered here is with spatially indexed data in which the dependence structure of observed random variables is characterized…
Graph Contrastive Learning (GCL) has emerged as a powerful paradigm for training Graph Neural Networks (GNNs) in the absence of task-specific labels. However, its scalability on large-scale graphs is hindered by the intensive message…
Covariate-adaptive randomization (CAR) procedures are frequently used in comparative studies to increase the covariate balance across treatment groups. However, because randomization inevitably uses the covariate information when forming…
Categorical Gini Correlation (CGC), introduced by Dang et al. (2020), is a novel dependence measure designed to quantify the association between a numerical variable and a categorical variable. It has appealing properties compared to…
Many probabilistic models that have an intractable normalizing constant may be extended to contain covariates. Since the evaluation of the exact likelihood is difficult or even impossible for these models, score matching was proposed to…
The perceptual loss has been widely used as an effective loss term in image synthesis tasks including image super-resolution, and style transfer. It was believed that the success lies in the high-level perceptual feature representations…
Graphical structures estimated by causal learning algorithms from time series data can provide misleading causal information if the causal timescale of the generating process fails to match the measurement timescale of the data. Existing…
In time-series analyses, particularly for finance, generalized autoregressive conditional heteroscedasticity (GARCH) models are widely applied statistical tools for modelling volatility clusters (i.e., periods of increased or decreased…
Finite Mixture of Regressions (FMR) models are among the most widely used approaches in dealing with the heterogeneity among the observations in regression problems. One of the limitations of current approaches is their inability to…
Bayesian hierarchical modeling is a natural framework to effectively integrate data and borrow information across groups. In this paper, we address problems related to density estimation and identifying clusters across related groups, by…
A general random effects model is proposed that allows for continuous as well as discrete distributions of the responses. Responses can be unrestricted continuous, bounded continuous, binary, ordered categorical or given in the form of…
This paper studies high-dimensional regression with two-way structured data. To estimate the high-dimensional coefficient vector, we propose the generalized matrix decomposition regression (GMDR) to efficiently leverage any auxiliary…
Complex-valued signals are used in the modeling of many systems in engineering and science, hence being of fundamental interest. Often, random complex-valued signals are considered to be proper. A proper complex random variable or process…