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The new ingredient of this paper is that we consider infinitely dimensional classes of functions and instead of the relative error setting, which was used in previous papers on norm discretization, we consider the absolute error setting. We…
The density weighted average derivative (DWAD) of a regression function is a canonical parameter of interest in economics. Classical first-order large sample distribution theory for kernel-based DWAD estimators relies on tuning parameter…
We propose modeling raw functional data as a mixture of a smooth function and a high-dimensional factor component. The conventional approach to retrieving the smooth function from the raw data is through various smoothing techniques.…
Conducting pairwise comparisons is a widely used approach in curating human perceptual preference data. Typically raters are instructed to make their choices according to a specific set of rules that address certain dimensions of image…
Recent works have proposed optimal subsampling algorithms to improve computational efficiency in large datasets and to design validation studies in the presence of measurement error. Existing approaches generally fall into two categories:…
In our era of enormous neural networks, empirical progress has been driven by the philosophy that more is better. Recent deep learning practice has found repeatedly that larger model size, more data, and more computation (resulting in lower…
In traditional models of supervised learning, the goal of a learner -- given examples from an arbitrary joint distribution on $\mathbb{R}^d \times \{\pm 1\}$ -- is to output a hypothesis that is competitive (to within $\epsilon$) of the…
Functional linear regression is an important topic in functional data analysis. It is commonly assumed that samples of the functional predictor are independent realizations of an underlying stochastic process, and are observed over a grid…
The notion of statistical depth has been extensively studied in multivariate and functional data over the past few decades. In contrast, the depth on temporal point process is still under-explored. The problem is challenging because a point…
Subsampling algorithms for various parametric regression models with massive data have been extensively investigated in recent years. However, all existing studies on subsampling heavily rely on clean massive data. In practical…
Smoothing is widely used approach for measurement noise reduction in spectral analysis. However, it suffers from signal distortion caused by peak suppression. A locally self-adjustive smoothing method is developed that retains sharp peaks…
Latent variable models serve as powerful tools to infer underlying dynamics from observed neural activity. Ideally, the inferred dynamics should align with true ones. However, due to the absence of ground truth data, prediction benchmarks…
Constructing confidence intervals for the value of an (unknown) optimal treatment policy is a fundamental problem in causal inference. Insight into the optimal policy value can guide the development of reward-maximizing, individualized…
Quantitative computational models play an increasingly important role in modern biology. Such models typically involve many free parameters, and assigning their values is often a substantial obstacle to model development. Directly measuring…
We study the prevalent problem when a test distribution differs from the training distribution. We consider a setting where our training set consists of a small number of sample domains, but where we have many samples in each domain. Our…
Deploying machine learning models in safety-critical domains poses a key challenge: ensuring reliable model performance on downstream user data without access to ground truth labels for direct validation. We propose the suitability filter,…
Randomized smoothing has been shown to provide good certified-robustness guarantees for high-dimensional classification problems. It uses the probabilities of predicting the top two most-likely classes around an input point under a…
We consider the estimation of the slope function in functional linear regression, where scalar responses are modeled in dependence of random functions. Cardot and Johannes [J. Multivariate Anal. 101 (2010) 395-408] have shown that a…
Organizations that own data face increasing legal liability for its discriminatory use against protected demographic groups, extending to contractual transactions involving third parties access and use of the data. This is problematic,…
Deep learning has exhibited superior performance for various tasks, especially for high-dimensional datasets, such as images. To understand this property, we investigate the approximation and estimation ability of deep learning on…