Related papers: Fast rates for empirical vector quantization
Recent results in quantization theory show that the mean-squared expected distortion can reach a rate of convergence of $\mathcal{O}(1/n)$, where $n$ is the sample size [see, e.g., IEEE Trans. Inform. Theory 60 (2014) 7279-7292 or Electron.…
Selecting appropriate regularization coefficients is critical to performance with respect to regularized empirical risk minimization problems. Existing theoretical approaches attempt to determine the coefficients in order for regularized…
The effect of errors in variables in empirical minimization is investigated. Given a loss $l$ and a set of decision rules $\mathcal{G}$, we prove a general upper bound for an empirical minimization based on a deconvolution kernel and a…
This paper studies fixed-rate randomized vector quantization under the constraint that the quantizer's output has a given fixed probability distribution. A general representation of randomized quantizers that includes the common models in…
In this paper, we adopt the eigenvector empirical spectral distribution (VESD) to investigate the limiting behavior of eigenvectors of a large dimensional Wigner matrix W_n. In particular, we derive the optimal bound for the rate of…
We study the convergence rate of the optimal quantization for a probability measure sequence $(\mu_{n})_{n\in\mathbb{N}^{*}}$ on $\mathbb{R}^{d}$ converging in the Wasserstein distance in two aspects: the first one is the convergence rate…
The distortion-rate performance of certain randomly-designed scalar quantizers is determined. The central results are the mean-squared error distortion and output entropy for quantizing a uniform random variable with thresholds drawn…
For $V : \mathbb{R}^d \to \mathbb{R}$ coercive, we study the convergence rate for the $L^1$-distance of the empiric minimizer, which is the true minimum of the function $V$ sampled with noise with a finite number $n$ of samples, to the…
Stochastic approximation is a foundation for many algorithms found in machine learning and optimization. It is in general slow to converge: the mean square error vanishes as $O(n^{-1})$. A deterministic counterpart known as quasi-stochastic…
We show the existence of variable-rate rate-distortion codes that meet the disortion constraint almost surely and are minimax, i.e., strongly, universal with respect to an unknown source distribution and a distortion measure that is…
The following critical phenomenon was recently discovered. When a memoryless source is compressed using a variable-length fixed-distortion code, the fastest convergence rate of the (pointwise) compression ratio to the optimal $R(D)$…
In this paper, the uniformly asymptotic normality for sample quantiles of associated random variables is investigated under some conditions on the decay of the covariances. We obtain the rate of normal approximation of order…
We design and mathematically analyze sampling-based algorithms for regularized loss minimization problems that are implementable in popular computational models for large data, in which the access to the data is restricted in some way. Our…
We consider the rates of convergence of the quenched central limit theorem for hitting times of one-dimensional random walks in a random environment. Previous results had identified polynomial upper bounds for the rates of decay which are…
We study realizable continual linear regression under random task orderings, a common setting for developing continual learning theory. In this setup, the worst-case expected loss after $k$ learning iterations admits a lower bound of…
In this paper, we analyze the convergence properties of the Lion optimizer. First, we establish that the Lion optimizer attains a convergence rate of $\mathcal{O}(d^{1/2}T^{-1/4})$ under standard assumptions, where $d$ denotes the problem…
We study a localized notion of uniform convergence known as an "optimistic rate" (Panchenko 2002; Srebro et al. 2010) for linear regression with Gaussian data. Our refined analysis avoids the hidden constant and logarithmic factor in…
We construct a novel estimator for the diffusion coefficient of the limiting homogenized equation, when observing the slow dynamics of a multiscale model, in the case when the slow dynamics are of bounded variation. Previous research…
We prove an upper bound for the convergence rate of the homogenization limit $\epsilon\to 0$ for a linear transmission problem for a advection-diffusion(-reaction) system posed in areas with low and high diffusivity, where $\epsilon$ is a…
The sampling, quantization, and estimation of a bounded dynamic-range bandlimited signal affected by additive independent Gaussian noise is studied in this work. For bandlimited signals, the distortion due to additive independent Gaussian…