相关论文: Density estimation for shift-invariant multidimens…

Given i.i.d samples from some unknown continuous density on hyper-rectangle $[0, 1]^d$, we attempt to learn a piecewise constant function that approximates this underlying density non-parametrically. Our density estimate is defined on a…

We study the {\em robust proper learning} of univariate log-concave distributions (over continuous and discrete domains). Given a set of samples drawn from an unknown target distribution, we want to compute a log-concave hypothesis…

Learning robust models under distribution shifts between training and test datasets is a fundamental challenge in machine learning. While learning invariant features across environments is a popular approach, it often assumes that these…

Covariate-shift generalization, a typical case in out-of-distribution (OOD) generalization, requires a good performance on the unknown test distribution, which varies from the accessible training distribution in the form of covariate shift.…

Learning dynamics from dissipative chaotic systems is notoriously difficult due to their inherent instability, as formalized by their positive Lyapunov exponents, which exponentially amplify errors in the learned dynamics. However, many of…

We study nonparametric density estimation in non-stationary drift settings. Given a sequence of independent samples taken from a distribution that gradually changes in time, the goal is to compute the best estimate for the current…

Dynamic decision-making under distributional shifts is of fundamental interest in theory and applications of reinforcement learning: The distribution of the environment in which the data is collected can differ from that of the environment…

Recent advances in deep learning from probability distributions successfully achieve classification or regression from distribution samples, thus invariant under permutation of the samples. The first contribution of the paper is to extend…

Deep neural networks have attained remarkable performance when applied to data that comes from the same distribution as that of the training set, but can significantly degrade otherwise. Therefore, detecting whether an example is…

The density ratio is an important metric for evaluating the relative likelihood of two probability distributions, with extensive applications in statistics and machine learning. However, existing estimation theories for density ratios often…

Recent advances have revealed that the rate of convergence of the expected test error in deep supervised learning decays as a function of the intrinsic dimension and not the dimension $d$ of the input space. Existing literature defines this…

While deep neural networks have made remarkable progress in various vision tasks, their performance typically deteriorates when tested in out-of-distribution (OOD) scenarios. Many OOD methods focus on extracting domain-invariant features…

A fundamental notion of distance between train and test distributions from the field of domain adaptation is discrepancy distance. While in general hard to compute, here we provide the first set of provably efficient algorithms for testing…

The manifold hypothesis asserts that data of interest in high-dimensional ambient spaces, such as image data, lies on unknown low-dimensional submanifolds. Diffusion models (DMs) -- which operate by convolving data with progressively larger…

Methods for anomaly detection of new physics processes are often limited to low-dimensional spaces due to the difficulty of learning high-dimensional probability densities. Particularly at the constituent level, incorporating desirable…

In the field of Machine Learning (ML) and data-driven applications, one of the significant challenge is the change in data distribution between the training and deployment stages, commonly known as distribution shift. This paper outlines…

Deep learning models lack shift invariance, making them sensitive to input shifts that cause changes in output. While recent techniques seek to address this for images, our findings show that these approaches fail to provide…

Consider discrete values of functions shifted by unobserved translation effects, which are independent realizations of a random variable with unknown distribution $\mu$, modeling the variability in the response of each individual. Our aim…

We prove that $\tilde{\Theta}(k d^2 / \varepsilon^2)$ samples are necessary and sufficient for learning a mixture of $k$ Gaussians in $\mathbb{R}^d$, up to error $\varepsilon$ in total variation distance. This improves both the known upper…

Accurate estimation of Intrinsic Dimensionality (ID) is of crucial importance in many data mining and machine learning tasks, including dimensionality reduction, outlier detection, similarity search and subspace clustering. However, since…