arXiv research

New method uses graphene transistors for efficient non-uniform random number generation.

Method generates random numbers from sensor noise, improving accuracy and speed.

We apply stochastic average gradient (SAG) algorithms for training conditional random fields (CRFs). We describe a practical implementation that uses structure in the CRF gradient to reduce the memory requirement of this linearly-convergent stochastic gradient method, propose a non-uniform sampling scheme that substant…

We study the effectiveness of non-uniform randomized feature selection in decision tree classification. We experimentally evaluate two feature selection methodologies, based on information extracted from the provided dataset: $(i)$ \emph{leverage scores-based} and $(ii)$ \emph{norm-based} feature selection. Experimenta…

Spectral algorithm recovers community structure in sparse hypergraphs.

Sharp threshold for exact recovery in non-uniform hypergraph stochastic block model.

In this work we study the degree distribution, the maximum vertex and edge flow in non-uniform random Delaunay triangulations when geodesic routing is used. We also investigate the vertex and edge flow in Erdös-Renyi random graphs, geometric random graphs, expanders and random $k$-regular graphs. Moreover we show that …

Validates conformal prediction for network data under non-uniform sampling.

Proves spectral gap bounds for Teichmüller geodesics on flat surfaces.

New method calculates Ricci curvature from distances between weighted volumes.

Hypergraph partitioning lies at the heart of a number of problems in machine learning and network sciences. Many algorithms for hypergraph partitioning have been proposed that extend standard approaches for graph partitioning to the case of hypergraphs. However, theoretical aspects of such methods have seldom received …

Simulates financial market orders using anomalous diffusion models.

This paper considers a new family of variational distributions motivated by Sklar's theorem. This family is based on new copula-like densities on the hypercube with non-uniform marginals which can be sampled efficiently, i.e. with a complexity linear in the dimension of state space. Then, the proposed variational densi…

The study finds non-uniform lattices with thin Hitchin representations in specific Lie groups.

New approach to adversarial robustness with non-uniform perturbations.

This work studies the robustness certification problem of neural network models, which aims to find certified adversary-free regions as large as possible around data points. In contrast to the existing approaches that seek regions bounded uniformly along all input features, we consider non-uniform bounds and use it to …

The notion of expense in Bayesian optimisation generally refers to the uniformly expensive cost of function evaluations over the whole search space. However, in some scenarios, the cost of evaluation for black-box objective functions is non-uniform since different inputs from search space may incur different costs for …

New method upsamples sparse, non-uniform point clouds more accurately.

Many stochastic optimization algorithms work by estimating the gradient of the cost function on the fly by sampling datapoints uniformly at random from a training set. However, the estimator might have a large variance, which inadvertently slows down the convergence rate of the algorithms. One way to reduce this varian…

New insights into variational inference using Monte Carlo estimates.

New approach finds minima of geodesic lengths for non-uniform fillings.

Study shows how non-uniform scaling affects persistence diagrams.

Unified framework for non-uniform materials evolving over time.

The paper studies random covers of torus knot complements and their statistical properties.

New rigidity theorem for product of lattices.

We consider the problem of finding the minimizer of a convex function $F: \mathbb R^d \rightarrow \mathbb R$ of the form $F(w) := \sum_{i=1}^n f_i(w) + R(w)$ where a low-rank factorization of $\nabla^2 f_i(w)$ is readily available. We consider the regime where $n \gg d$. As second-order methods prove to be effective in…

ABC algorithms involve a large number of simulations from the model of interest, which can be very computationally costly. This paper summarises the lazy ABC algorithm of Prangle (2015), which reduces the computational demand by abandoning many unpromising simulations before completion. By using a random stopping decis…

Non-uniform lattices in PU(n,1) cannot geometrically act on CAT(0) cube complexes.

We study primal-dual type stochastic optimization algorithms with non-uniform sampling. Our main theoretical contribution in this paper is to present a convergence analysis of Stochastic Primal Dual Coordinate (SPDC) Method with arbitrary sampling. Based on this theoretical framework, we propose Optimality Violation-ba…

Paper improves anomaly detection by using non-uniform random choices in isolation forests.

New algorithm achieves strong consistency in binary non-uniform hypergraph classification.

New method detects communities in complex hypergraphs, matching theoretical limits.

Corrects bias in random sampling matrices for improved ML methods.

We present a novel method for neural network quantization that emulates a non-uniform $k$-quantile quantizer, which adapts to the distribution of the quantized parameters. Our approach provides a novel alternative to the existing uniform quantization techniques for neural networks. We suggest to compare the results as …

The paper models social networks with varying levels of reciprocity.

We propose a new randomized coordinate descent method for a convex optimization template with broad applications. Our analysis relies on a novel combination of four ideas applied to the primal-dual gap function: smoothing, acceleration, homotopy, and coordinate descent with non-uniform sampling. As a result, our method…

We prove that if $G$ is a non-uniform lattice in a rank-one semi-simple Lie group $\ne Isom(\H^2_\R)$ then $G$ is quasi-isometrically co-Hopf. This means that every quasi-isometric embedding $G\to G$ is coarsely onto and thus is a quasi-isometry.

Improved sampling accuracy in SG-MCMC methods via non-uniform gradient subsampling.

A groupoid $Ω\left( \mathcal{B} \right)$ called material groupoid is naturally associated to any simple body $\mathcal{B}$. The material distribution is introduced due to the (possible) lack of differentiability of the material groupoid. Thus, the inclusion of these new objects in the theory of material bodies opens th…

This work investigates the training of conditional random fields (CRFs) via the stochastic dual coordinate ascent (SDCA) algorithm of Shalev-Shwartz and Zhang (2016). SDCA enjoys a linear convergence rate and a strong empirical performance for binary classification problems. However, it has never been used to train CRF…

In this note, we study deformations of a non-uniform real hyperbolic lattice in quaternionic hyperbolic spaces. Specially we show that the representations of the fundamental group of the figure eight knot complement into PU(2,1) cannot be deformed in $PSp(2,1)$ out of PU(2,1) up to conjugacy.

We construct a three-point compact finite difference scheme on a non-uniform mesh for the time-fractional Black-Scholes equation. We show that for special graded meshes used in finance, the Tavella-Randall and the quadratic meshes the numerical solution has a fourth-order accuracy in space. Numerical experiments are di…

Paper extracts features from time series to improve forecasting accuracy.

This study examines how randomness affects machine learning model performance.

The paper achieves nearly optimal regret bounds for contextual multinomial logit bandits.

Improved matrix completion for non-uniformly sampled data.

New loss function equivalence reveals PER's uniform sampling can be improved.

We address the following problem: given two smooth densities on a manifold, find an optimal diffeomorphism that transforms one density into the other. Our framework builds on connections between the Fisher-Rao information metric on the space of probability densities and right-invariant metrics on the infinite-dimension…