Related papers: Exact Distribution-Free Hypothesis Tests for the R…
We address the consistency of a kernel ridge regression estimate of the conditional mean embedding (CME), which is an embedding of the conditional distribution of $Y$ given $X$ into a target reproducing kernel Hilbert space $\mathcal{H}_Y$.…
We consider the problem of distributed binary hypothesis testing of two sequences that are generated by an i.i.d. doubly-binary symmetric source. Each sequence is observed by a different terminal. The two hypotheses correspond to different…
We propose a vector-valued regression problem whose solution is equivalent to the reproducing kernel Hilbert space (RKHS) embedding of the Bayesian posterior distribution. This equivalence provides a new understanding of kernel Bayesian…
We present a novel distributionally robust framework for dynamic programming that uses kernel methods to design feedback control policies. Specifically, we leverage kernel mean embedding to map the transition probabilities governing the…
A distributed binary hypothesis testing problem, in which multiple observers transmit their observations to a detector over noisy channels, is studied. Given its own side information, the goal of the detector is to decide between two…
The problem of error density estimation for a functional single index model with dependent errors is studied. A Bayesian method is utilized to simultaneously estimate the bandwidths in the kernel-form error density and regression function,…
Misclassification of binary responses, if ignored, may severely bias the maximum likelihood estimators (MLE) of regression parameters. For such data, a binary regression model incorporating misclassification probabilities is extensively…
Distributed machine learning systems have been receiving increasing attentions for their efficiency to process large scale data. Many distributed frameworks have been proposed for different machine learning tasks. In this paper, we study…
While the performance of machine learning systems has experienced significant improvement in recent years, relatively little attention has been paid to the fundamental question: to what extent can we improve our models? This paper provides…
The integrated conditional moment (ICM) test is a classical and widely used method for assessing the adequacy of regression models. Although it performs well in fixed-dimension settings, its behavior changes dramatically when the predictor…
We propose a methodology for testing linear hypothesis in high-dimensional linear models. The proposed test does not impose any restriction on the size of the model, i.e. model sparsity or the loading vector representing the hypothesis.…
Inference for functional linear models in the presence of heteroscedastic errors has received insufficient attention given its practical importance; in fact, even a central limit theorem has not been studied in this case. At issue,…
In regression analysis under artificial neural networks, the prediction performance depends on determining the appropriate weights between layers. As randomly initialized weights are updated during back-propagation using the gradient…
Most machine learning algorithms, such as classification or regression, treat the individual data point as the object of interest. Here we consider extending machine learning algorithms to operate on groups of data points. We suggest…
Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. When the kernel is characteristic, mean embeddings can be used…
In real-world applications, the limited availability of labeled outcomes presents significant challenges for statistical inference due to high collection costs, technical barriers, and other constraints. In this work, we propose a method to…
We study how the training data distribution affects confidence and performance in image classification models. We introduce Embedding Density, a model-agnostic framework that estimates prediction confidence by measuring the distance of test…
The problem of binary hypothesis testing between two probability measures is considered. New sharp bounds are derived for the best achievable error probability of such tests based on independent and identically distributed observations.…
Recently a distribution free approach for testing parametric hypotheses based on unitary transformations has been suggested in \cite{Khm13, Khm16, Khm17} and further studied in \cite{Ngu17} and \cite{Rob19}. In this note we show that the…
Motivated by applications, we consider here new operator theoretic approaches to Conditional mean embeddings (CME). Our present results combine a spectral analysis-based optimization scheme with the use of kernels, stochastic processes, and…