Related papers: Universal Perfect Samplers for Incremental Streams
We provide a new upper bound for sampling numbers $(g_n)_{n\in \mathbb{N}}$ associated to the compact embedding of a separable reproducing kernel Hilbert space into the space of square integrable functions. There are universal constants…
Gaussian Boson Sampling (GBS) generate random samples of photon-click patterns from a class of probability distributions that are hard for a classical computer to sample from. Despite heroic demonstrations for quantum supremacy using GBS,…
Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimization problem over all probability measures, and an initial…
Let $G$ be a finite group generated by $k$ elements. The well-known product replacement algorithm provides an effective method for sampling generating sets of $G$. We study a refinement of this algorithm that is designed to output…
Graph sampling is the problem of choosing a node subset via sampling matrix $\mathbf{H} \in \{0,1\}^{K \times N}$ to collect samples $\mathbf{y} = \mathbf{H} \mathbf{x} \in \mathbb{R}^K$, $K < N$, so that the target signal $\mathbf{x} \in…
The $G^{+}$ method is a new method, a powerful one, for the study of (homogeneous and nonhomogeneous) products of nonnegative matrices -- for problems on the products of nonnegative matrices. To study such products, new classes of matrices…
The canonical approach in generative modeling is to split model fitting into two blocks: define first how to sample noise (e.g. Gaussian) and choose next what to do with it (e.g. using a single map or flows). We explore in this work an…
Gaussian mixture models (GMMs) are fundamental tools in statistical and data sciences. We study the moments of multivariate Gaussians and GMMs. The $d$-th moment of an $n$-dimensional random variable is a symmetric $d$-way tensor of size…
Let p be a prime number. Let G be a finite abelian p-group of exponent n (written additively) and A be a non-empty subset of $]n[:= \{1,2,..., n\}$ such that elements of A are incongruent modulo p and non-zero modulo p. Let $k \geq…
Graph Convolutional Networks (GCNs) are powerful models for learning representations of attributed graphs. To scale GCNs to large graphs, state-of-the-art methods use various layer sampling techniques to alleviate the "neighbor explosion"…
In this work we investigate stochastic non-convex optimization problems where the objective is an expectation over smooth loss functions, and the goal is to find an approximate stationary point. The most popular approach to handling such…
Generative neural samplers are probabilistic models that implement sampling using feedforward neural networks: they take a random input vector and produce a sample from a probability distribution defined by the network weights. These models…
We study the complexity of sampling from a distribution over all index subsets of the set $\{1,...,n\}$ with the probability of a subset $S$ proportional to the determinant of the submatrix $\mathbf{L}_S$ of some $n\times n$ p.s.d. matrix…
Neural Collaborative Filtering models are widely used in recommender systems but are typically trained under static settings, assuming fixed data distributions. This limits their applicability in dynamic environments where user preferences…
Diffusion models have become emerging generative models. Their sampling process involves multiple steps, and in each step the models predict the noise from a noisy sample. When the models make prediction, the output deviates from the ground…
While Gaussian processes (GPs) are the method of choice for regression tasks, they also come with practical difficulties, as inference cost scales cubic in time and quadratic in memory. In this paper, we introduce a natural and expressive…
We develop and analyze the Generalized Multiplicative Gradient (GMG) method for solving a class of convex optimization problems over symmetric cones, where the objective function does not have Lipschitz gradient over the feasible region.…
We study nonuniform sampling in shift-invariant spaces and the construction of Gabor frames with respect to the class of totally positive functions whose Fourier transform factors as $ \hat g(\xi)= \prod_{j=1}^n (1+2\pi i\delta_j\xi)^{-1}…
Video Moment Retrieval (VMR) aims to localize temporal segments in videos that correspond to a natural language query, but typically assumes only a single matching moment for each query. This assumption does not always hold in real-world…
Subgraph-wise sampling -- a promising class of mini-batch training techniques for graph neural networks (GNNs -- is critical for real-world applications. During the message passing (MP) in GNNs, subgraph-wise sampling methods discard…