This paper addresses challenges in robust transfer learning stemming from ambiguity in Bayes classifiers and weak transferable signals between the target and source distribution. We introduce a novel quantity called the ''ambiguity level'' that measures the discrepancy between the target and source regression functions, propose a simple transfer learning procedure, and establish a general theorem that shows how this new quantity is related to the transferability of learning in terms of risk improvements. Our proposed ''Transfer Around Boundary'' (TAB) model, with a threshold balancing the performance of target and source data, is shown to be both efficient and robust, improving classification while avoiding negative transfer. Moreover, we demonstrate the effectiveness of the TAB model on non-parametric classification and logistic regression tasks, achieving upper bounds which are optimal up to logarithmic factors. Simulation studies lend further support to the effectiveness of TAB. We also provide simple approaches to bound the excess misclassification error without the need for specialized knowledge in transfer learning.

While the test-negative design (TND), which is routinely used for monitoring seasonal flu vaccine effectiveness (VE), has recently become integral to COVID-19 vaccine surveillance, it is susceptible to selection bias due to outcome-dependent sampling. Some studies have addressed the identifiability and estimation of causal parameters under the TND, but efficiency bounds for nonparametric estimators of the target parameter under the unconfoundedness assumption have not yet been investigated. We propose a one-step doubly robust and locally efficient estimator called TNDDR (TND doubly robust), which utilizes sample splitting and can incorporate machine learning techniques to estimate the nuisance functions. We derive the efficient influence function (EIF) for the marginal expectation of the outcome under a vaccination intervention, explore the von Mises expansion, and establish the conditions for $\sqrt{n}-$consistency, asymptotic normality and double robustness of TNDDR. The proposed TNDDR is supported by both theoretical and empirical justifications, and we apply it to estimate COVID-19 VE in an administrative dataset of community-dwelling older people (aged $\geq 60$y) in the province of Qu\'ebec, Canada.

The premise of identifiable and causal representation learning is to improve the current representation learning paradigm in terms of generalizability or robustness. Despite recent progress in questions of identifiability, more theoretical results demonstrating concrete advantages of these methods for downstream tasks are needed. In this paper, we consider the task of intervention extrapolation: predicting how interventions affect an outcome, even when those interventions are not observed at training time, and show that identifiable representations can provide an effective solution to this task even if the interventions affect the outcome non-linearly. Our setup includes an outcome Y, observed features X, which are generated as a non-linear transformation of latent features Z, and exogenous action variables A, which influence Z. The objective of intervention extrapolation is to predict how interventions on A that lie outside the training support of A affect Y. Here, extrapolation becomes possible if the effect of A on Z is linear and the residual when regressing Z on A has full support. As Z is latent, we combine the task of intervention extrapolation with identifiable representation learning, which we call Rep4Ex: we aim to map the observed features X into a subspace that allows for non-linear extrapolation in A. We show using Wiener's Tauberian theorem that the hidden representation is identifiable up to an affine transformation in Z-space, which is sufficient for intervention extrapolation. The identifiability is characterized by a novel constraint describing the linearity assumption of A on Z. Based on this insight, we propose a method that enforces the linear invariance constraint and can be combined with any type of autoencoder. We validate our theoretical findings through synthetic experiments and show that our approach succeeds in predicting the effects of unseen interventions.

Water resources are essential for sustaining human livelihoods and environmental well being. Accurate water quality prediction plays a pivotal role in effective resource management and pollution mitigation. In this study, we assess the effectiveness of five distinct predictive models linear regression, Random Forest, XGBoost, LightGBM, and MLP neural network, in forecasting pH values within the geographical context of Georgia, USA. Notably, LightGBM emerges as the top performing model, achieving the highest average precision. Our analysis underscores the supremacy of tree-based models in addressing regression challenges, while revealing the sensitivity of MLP neural networks to feature scaling. Intriguingly, our findings shed light on a counterintuitive discovery: machine learning models, which do not explicitly account for time dependencies and spatial considerations, outperform spatial temporal models. This unexpected superiority of machine learning models challenges conventional assumptions and highlights their potential for practical applications in water quality prediction. Our research aims to establish a robust predictive pipeline accessible to both data science experts and those without domain specific knowledge. In essence, we present a novel perspective on achieving high prediction accuracy and interpretability in data science methodologies. Through this study, we redefine the boundaries of water quality forecasting, emphasizing the significance of data driven approaches over traditional spatial temporal models. Our findings offer valuable insights into the evolving landscape of water resource management and environmental protection.

Low-rank multivariate regression (LRMR) is an important statistical learning model that combines highly correlated tasks as a multiresponse regression problem with low-rank priori on the coefficient matrix. In this paper, we study quantized LRMR, a practical setting where the responses and/or the covariates are discretized to finite precision. We focus on the estimation of the underlying coefficient matrix. To make consistent estimator that could achieve arbitrarily small error possible, we employ uniform quantization with random dithering, i.e., we add appropriate random noise to the data before quantization. Specifically, uniform dither and triangular dither are used for responses and covariates, respectively. Based on the quantized data, we propose the constrained Lasso and regularized Lasso estimators, and derive the non-asymptotic error bounds. With the aid of dithering, the estimators achieve minimax optimal rate, while quantization only slightly worsens the multiplicative factor in the error rate. Moreover, we extend our results to a low-rank regression model with matrix responses. We corroborate and demonstrate our theoretical results via simulations on synthetic data or image restoration.

When artificial neural networks have demonstrated exceptional practical success in a variety of domains, investigations into their theoretical characteristics, such as their approximation power, statistical properties, and generalization performance, have concurrently made significant strides. In this paper, we construct a novel theory for understanding the effectiveness of neural networks, which offers a perspective distinct from prior research. Specifically, we explore the rationale underlying a common practice during the construction of neural network models: sample splitting. Our findings indicate that the optimal hyperparameters derived from sample splitting can enable a neural network model that asymptotically minimizes the prediction risk. We conduct extensive experiments across different application scenarios and network architectures, and the results manifest our theory's effectiveness.

In the 1950s, Barlow and Attneave hypothesised a link between biological vision and information maximisation. Following Shannon, information was defined using the probability of natural images. A number of physiological and psychophysical phenomena have been derived ever since from principles like info-max, efficient coding, or optimal denoising. However, it remains unclear how this link is expressed in mathematical terms from image probability. First, classical derivations were subjected to strong assumptions on the probability models and on the behaviour of the sensors. Moreover, the direct evaluation of the hypothesis was limited by the inability of the classical image models to deliver accurate estimates of the probability. In this work we directly evaluate image probabilities using an advanced generative model for natural images, and we analyse how probability-related factors can be combined to predict human perception via sensitivity of state-of-the-art subjective image quality metrics. We use information theory and regression analysis to find a combination of just two probability-related factors that achieves 0.8 correlation with subjective metrics. This probability-based sensitivity is psychophysically validated by reproducing the basic trends of the Contrast Sensitivity Function, its suprathreshold variation, and trends of the Weber-law and masking.

Solving chance-constrained stochastic optimal control problems is a significant challenge in control. This is because no analytical solutions exist for up to a handful of special cases. A common and computationally efficient approach for tackling chance-constrained stochastic optimal control problems consists of reformulating the chance constraints as hard constraints with a constraint-tightening parameter. However, in such approaches, the choice of constraint-tightening parameter remains challenging, and guarantees can mostly be obtained assuming that the process noise distribution is known a priori. Moreover, the chance constraints are often not tightly satisfied, leading to unnecessarily high costs. This work proposes a data-driven approach for learning the constraint-tightening parameters online during control. To this end, we reformulate the choice of constraint-tightening parameter for the closed-loop as a binary regression problem. We then leverage a highly expressive \gls{gp} model for binary regression to approximate the smallest constraint-tightening parameters that satisfy the chance constraints. By tuning the algorithm parameters appropriately, we show that the resulting constraint-tightening parameters satisfy the chance constraints up to an arbitrarily small margin with high probability. Our approach yields constraint-tightening parameters that tightly satisfy the chance constraints in numerical experiments, resulting in a lower average cost than three other state-of-the-art approaches.

This paper proposes a latent prompt Transformer model for solving challenging optimization problems such as molecule design, where the goal is to find molecules with optimal values of a target chemical or biological property that can be computed by an existing software. Our proposed model consists of three components. (1) A latent vector whose prior distribution is modeled by a Unet transformation of a Gaussian white noise vector. (2) A molecule generation model that generates the string-based representation of molecule conditional on the latent vector in (1). We adopt the causal Transformer model that takes the latent vector in (1) as prompt. (3) A property prediction model that predicts the value of the target property of a molecule based on a non-linear regression on the latent vector in (1). We call the proposed model the latent prompt Transformer model. After initial training of the model on existing molecules and their property values, we then gradually shift the model distribution towards the region that supports desired values of the target property for the purpose of molecule design. Our experiments show that our proposed model achieves state of the art performances on several benchmark molecule design tasks.

Given the growing prevalence of diabetes, there has been significant interest in determining how diabetes affects instrumental daily functions, like driving. Complication of glucose control in diabetes includes hypoglycemic and hyperglycemic episodes, which may impair cognitive and psychomotor functions needed for safe driving. The goal of this paper was to determine patterns of diabetes speed behavior during acute glucose to drivers with diabetes who were euglycemic or control drivers without diabetes in a naturalistic driving environment. By employing distribution-based analytic methods which capture distribution patterns, our study advances prior literature that has focused on conventional approach of average speed to explore speed deviation patterns.