arXiv research

Detects model changes in machine learning with empirical difference test.

Paper defends machine learning models from adversarial attacks using GLRT.

Develops GLRT for defending against adversarial attacks in hypothesis testing.

Two algorithms improve performance in piecewise-stationary cascading bandits.

This letter presents the sparse vector signal detection from one bit compressed sensing measurements, in contrast to the previous works which deal with scalar signal detection. In this letter, available results are extended to the vector case and the GLRT detector and the optimal quantizer design are obtained. Also, a …

We study the problem of detecting a change in the mean of one-dimensional Gaussian process data. This problem is investigated in the setting of increasing domain (customarily employed in time series analysis) and in the setting of fixed domain (typically arising in spatial data analysis). We propose a detection method …

Kernel method is a very powerful tool in machine learning. The trick of kernel has been effectively and extensively applied in many areas of machine learning, such as support vector machine (SVM) and kernel principal component analysis (kernel PCA). Kernel trick is to define a kernel function which relies on the inner-…

New algorithm detects changes in combinatorial semi-bandit rewards.

Proposes incorporating noise sources in machine learning evaluation for more reliable conclusions.

Paper connects neural network score approximation to reverse diffusion model distribution approximation.

The study provides conditions for approximating Riemannian manifolds with polyhedral metrics.

Paper proposes a new adaptive multiscale value function approximation for reinforcement learning.

Optimal function approximation with Relu neural networks achieves minimal error.

Geometric Gaussian approximations capture any distribution.

Paper proposes MCMA architecture for neural approximate computing with higher invocation rate and energy savings.

Deep learning networks are approximated using dynamical systems theory.

Method approximates Riemannian barycenter on manifolds.

Efficiently reduces tensor ranks using mean-field approximation.

Study approximates unknown function levels with queries.

We study sparse approximate solutions to convex optimization problems. It is known that in many engineering applications researchers are interested in an approximate solution of an optimization problem as a linear combination of elements from a given system of elements. There is an increasing interest in building such …

Softmax attention approximates complex functions and subsumes many known universal approximators.

Deviation inequalities for stochastic approximation methods.

Improved matrix approximation using randomized algorithms.

Approximate symmetries of geodesic equations on 2-spheres are studied. These are the symmetries of the perturbed geodesic equations which represent approximate path of a particle rather than exact path. After giving the exact symmetries of the geodesic equations, two different approaches to study the approximate symmet…

We are concerned with an approximation problem for a symmetric positive semidefinite matrix due to motivation from a class of nonlinear machine learning methods. We discuss an approximation approach that we call {matrix ridge approximation}. In particular, we define the matrix ridge approximation as an incomplete matri…

Transformers use ReLUs to approximate softmax efficiently.

Approximating complex curves with simple parametric curves is widely used in CAGD, CG, and CNC. This paper presents an algorithm to compute a certified approximation to a given parametric space curve with cubic B-spline curves. By certified, we mean that the approximation can approximate the given curve to any given pr…

Recently, variational approximations such as the mean field approximation have received much interest. We extend the standard mean field method by using an approximating distribution that factorises into cluster potentials. This includes undirected graphs, directed acyclic graphs and junction trees. We derive generaliz…

Adaptive approximations improve variational inference for complex models.

Non-negative $L_1$-approximating polynomials for Gaussian distributions are proven for certain classes of sets.

Paper analyzes normal approximation for two-timescale stochastic algorithms, revealing interaction between fast and slow timescales.

Paper introduces new approximations for lognormal sums, matching comonotonicity and moments.

One-pass algorithm finds small subset for $\ell_p$ subspace approximation with additive error.

We are interested in approximation of a multivariate function $f(x_1,\dots,x_d)$ by linear combinations of products $u^1(x_1)\cdots u^d(x_d)$ of univariate functions $u^i(x_i)$, $i=1,\dots,d$. In the case $d=2$ it is a classical problem of bilinear approximation. In the case of approximation in the $L_2$ space the bili…

A new method for efficient Gaussian process inference using sparse approximations.

In this paper, we propose a low-rank approximation method based on discrete least-squares for the approximation of a multivariate function from random, noisy-free observations. Sparsity inducing regularization techniques are used within classical algorithms for low-rank approximation in order to exploit the possible sp…

Neural network based approximate computing is a universal architecture promising to gain tremendous energy-efficiency for many error resilient applications. To guarantee the approximation quality, existing works deploy two neural networks (NNs), e.g., an approximator and a predictor. The approximator provides the appro…

Low-precision quantization improves kernel approximation under memory constraints.

The paper approximates supply curves using a one-step basis method.

The paper defines a new concept of approximability for Lagrangian submanifolds.

Boosting Nyström improves accuracy of matrix approximations.

High-probability bound for distributed stochastic approximation tracking error.

Nyström KPCA balances computational efficiency and statistical accuracy.

Deep ReLU networks can approximate smooth functions nearly optimally.

Improves Laplace approximation for Bayesian inference on Riemannian manifolds.

We approximate derivatives of functions on manifolds by embedding them and applying vector-valued operators.

We discuss Bayesian methods for learning Bayesian networks when data sets are incomplete. In particular, we examine asymptotic approximations for the marginal likelihood of incomplete data given a Bayesian network. We consider the Laplace approximation and the less accurate but more efficient BIC/MDL approximation. We …

Proposes efficient Gaussian approximations for non-Gaussian likelihoods.