Related papers: A Variance-Based Analysis of Sample Complexity for…
Sampled-data (SD) systems, which are composed of both discrete- and continuous-time components, are arguably one of the most common classes of cyberphysical systems in practice; most modern controllers are implemented on digital platforms…
We introduce the coverage correlation coefficient, a novel nonparametric measure of statistical association designed to quantifies the extent to which two random variables have a joint distribution concentrated on a singular subset with…
This paper investigates the soft covering lemma under both the relative entropy and the total variation distance as the measures of deviation. The exact order of the expected deviation of the random i.i.d. code for the soft covering problem…
We consider the problem of $L_p$-testing of class of bounded derivative properties over hypergrid domain with points distributed according to some product distribution. This class includes monotonicity, the Lipschitz property,…
The algorithmic theory of randomness is well developed when the underlying space is the set of finite or infinite sequences and the underlying probability distribution is the uniform distribution or a computable distribution. These…
Diffusion models have become the most popular approach to deep generative modeling of images, largely due to their empirical performance and reliability. From a theoretical standpoint, a number of recent works have studied the iteration…
While standard statistical inference techniques and machine learning generalization bounds assume that tests are run on data selected independently of the hypotheses, practical data analysis and machine learning are usually iterative and…
We study the problem of sampling from a $d$-dimensional distribution with density $p(x)\propto e^{-f(x)}$, which does not necessarily satisfy good isoperimetric conditions. Specifically, we show that for any $L,M$ satisfying $LM\ge d\ge 5$,…
We discuss a graph-based approach for testing spatial point patterns. This approach falls under the category of data-random graphs, which have been introduced and used for statistical pattern recognition in recent years. Our goal is to test…
Spectral clustering is a fundamental method for graph partitioning, but its reliance on eigenvector computation limits scalability to massive graphs. Classical sparsification methods preserve spectral properties by sampling edges…
This paper investigates the robust optimal control of sampled-data stochastic systems with multiplicative noise and distributional ambiguity. We consider a class of discrete-time optimal control problems where the controller \emph{jointly}…
The accuracy of deep learning, i.e., deep neural networks, can be characterized by dividing the total error into three main types: approximation error, optimization error, and generalization error. Whereas there are some satisfactory…
Most entropy measures depend on the spread of the probability distribution over the sample space $\mathcal{X}$, and the maximum entropy achievable scales proportionately with the sample space cardinality $|\mathcal{X}|$. For a finite…
We study the hard-core model defined on independent sets, where each independent set I in a graph G is weighted proportionally to $\lambda^{|I|}$, for a positive real parameter $\lambda$. For large $\lambda$, computing the partition…
This paper proves that robustness implies generalization via data-dependent generalization bounds. As a result, robustness and generalization are shown to be connected closely in a data-dependent manner. Our bounds improve previous bounds…
Estimating the data uncertainty in regression tasks is often done by learning a quantile function or a prediction interval of the true label conditioned on the input. It is frequently observed that quantile regression -- a vanilla algorithm…
Given a probability distribution P, what is the minimum amount of bits needed to store a value x sampled according to P, such that x can later be recovered (except with some small probability)? Or, what is the maximum amount of uniform…
This paper focuses on understanding how the generalization error scales with the amount of the training data for deep neural networks (DNNs). Existing techniques in statistical learning require computation of capacity measures, such as VC…
We analyse the entanglement structure of states generated by random constant-depth two-dimensional quantum circuits, followed by projective measurements of a subset of sites. By deriving a rigorous lower bound on the average entanglement…
We prove optimal sampling bounds achieving $(1\pm\varepsilon)$-relative error for a broad class of Lipschitz continuous classification loss functions under various regularization terms. This includes important functions such as logistic and…