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Small area estimators that ignore the sampling design lack design consistency when the sampling mechanism is complex and may be severely biased under informative designs. Existing procedures that account for the survey weights under…

Maximum likelihood estimation in nonlinear models can exhibit substantial instability in finite samples when the data provide limited information about certain parameters. Such instability is driven by rare but extreme realizations of the…

We re-examine the traditional Mean-Squared Error (MSE) forecasting paradigm by formally integrating an accuracy-timeliness trade-off: accuracy is defined by MSE (or target correlation) and timeliness by advancement (or phase excess). While…

To glean the benefits offered by massive multi-input multi-output (MIMO) systems, channel state information must be accurately acquired. Despite the high accuracy, the computational complexity of classical linear minimum mean squared error…

Pre-training Large Language Models (LLMs) on web-scale datasets becomes fundamental for advancing general-purpose AI. In contrast, enhancing their predictive performance on downstream tasks typically involves adapting their knowledge…

Driven by recent advances in artificial intelligence (AI), a growing literature has demonstrated the potential for using large language models (LLMs) as scalable surrogates to generate human-like responses in many business applications. Two…

The maximum likelihood (ML) estimator can be applied to localize a target mobile device using the RSS and TOA. However, the ML estimator for the RSS-TOA-based target localization problem is nonconvex and nonlinear, having no analytical…

Estimation under model misspecification arises in many signal processing problems, where the assumed observation model deviates from the true data-generating mechanism due to errors or simplifications. The misspecified Cram\'er-Rao bound…

Datasets in the fields of climate and environment are often very large and irregularly spaced. To model such datasets, the widely used Gaussian process models in spatial statis- tics face tremendous challenges due to the prohibitive…

Large language models (LLMs) exhibit remarkable capabilities across diverse tasks, yet aligning them efficiently and effectively with human expectations remains a critical challenge. This thesis advances LLM alignment by introducing novel…

This thesis designs a prediction system based on matrix factorization to predict the classification accuracy of a specific model on a particular dataset. In this thesis, we conduct comprehensive empirical research on more than fifty…

Recent frontier large language models predominantly rely on Mixture-of-Experts (MoE) architectures. Despite empirical progress, there is still no principled understanding of how hyperparameters should scale with network width $N$, expert…

In this paper, we mainly focus on the penalized maximum likelihood estimation (MLE) of the high-dimensional approximate factor model. Since the current estimation procedure can not guarantee the positive definiteness of the error covariance…

Mixture of Experts (MoE) are successful models for modeling heterogeneous data in many statistical learning problems including regression, clustering and classification. Generally fitted by maximum likelihood estimation via the well-known…

This paper considers probabilistic estimation of a low-rank matrix from non-linear element-wise measurements of its elements. We derive the corresponding approximate message passing (AMP) algorithm and its state evolution. Relying on…

The standard paradigm of neural language generation adopts maximum likelihood estimation (MLE) as the optimizing method. From a distributional view, MLE in fact minimizes the Kullback-Leibler divergence (KLD) between the distribution of the…

Many complex multi-target prediction problems that concern large target spaces are characterised by a need for efficient prediction strategies that avoid the computation of predictions for all targets explicitly. Examples of such problems…

Structural pruning techniques are essential for deploying multimodal large language models (MLLMs) across various hardware platforms, from edge devices to cloud servers. However, current pruning methods typically determine optimal…

Likelihood-free inference methods typically make use of a distance between simulated and real data. A common example is the maximum mean discrepancy (MMD), which has previously been used for approximate Bayesian computation, minimum…

In the missing data literature, the Maximum Likelihood Estimator (MLE) is celebrated for its ignorability property under missing at random (MAR) data. However, its sensitivity to misspecification of the (complete) data model, even under…