Related papers: Approximating Euler Totient Function using Linear …

Under a partially linear models we study a family of robust estimates for the regression parameter and the regression function when some of the predictor variables take values on a Riemannian manifold. We obtain the consistency and the…

We present a supervised learning model to calibrate the photon collection rate during the fluorescence imaging of cold atoms. The linear regression model finds the collection rate at each location on the sensor such that the atomic…

Auditing mechanisms for differential privacy use probabilistic means to empirically estimate the privacy level of an algorithm. For private machine learning, existing auditing mechanisms are tight: the empirical privacy estimate (nearly)…

Modern technologies are producing datasets with complex intrinsic structures, and they can be naturally represented as matrices instead of vectors. To preserve the latent data structures during processing, modern regression approaches…

To accelerate kernel methods, we propose a near input sparsity time algorithm for sampling the high-dimensional feature space implicitly defined by a kernel transformation. Our main contribution is an importance sampling method for…

We investigate robust nonparametric regression in the presence of heavy-tailed noise, where the hypothesis class may contain unbounded functions and robustness is ensured via a robust loss function $\ell_\sigma$. Using Huber regression as a…

Machine learning (ML) models are increasingly deployed in cybersecurity applications such as phishing detection and network intrusion prevention. However, these models remain vulnerable to adversarial perturbations small, deliberate input…

Remote state estimation in cyber-physical systems is often vulnerable to cyber-attacks due to wireless connections between sensors and computing units. In such scenarios, adversaries compromise the system by injecting false data or blocking…

Stochastic processes defined on integer valued state spaces are popular within the physical and biological sciences. These models are necessary for capturing the dynamics of small systems where the individual nature of the populations…

We consider the problem of approximating the regression function $f_\mu:\, \Omega \to Y$ from noisy $\mu$-distributed vector-valued data $(\omega_m,y_m)\in\Omega\times Y$ by an online learning algorithm using a reproducing kernel Hilbert…

We introduce a Fourier-based fast algorithm for Gaussian process regression in low dimensions. It approximates a translationally-invariant covariance kernel by complex exponentials on an equispaced Cartesian frequency grid of $M$ nodes.…

Kernel methods represent one of the most powerful tools in machine learning to tackle problems expressed in terms of function values and derivatives due to their capability to represent and model complex relations. While these methods show…

Recently, there has been considerable progress on designing algorithms with provable guarantees -- typically using linear algebraic methods -- for parameter learning in latent variable models. But designing provable algorithms for inference…

This paper introduces a consistent estimator and rate of convergence for the precision matrix of asset returns in large portfolios using a non-linear factor model within the deep learning framework. Our estimator remains valid even in low…

In this thesis, several linear and non-linear machine learning attacks on optical physical unclonable functions (PUFs) are presented. To this end, a simulation of such a PUF is implemented to generate a variety of datasets that differ in…

Complex phenomena in engineering and the sciences are often modeled with computationally intensive feed-forward simulations for which a tractable analytic likelihood does not exist. In these cases, it is sometimes necessary to estimate an…

We propose a general algorithm for approximating nonstandard Bayesian posterior distributions. The algorithm minimizes the Kullback-Leibler divergence of an approximating distribution to the intractable posterior distribution. Our method…

We study the generalized trace regression with a near low-rank regression coefficient matrix, which extends notion of sparsity for regression coefficient vectors. Specifically, given a matrix covariate $X$, the probability density function…

We obtain an upper bound for the sum $\sum_{n\leq N} (a_{n}/\varphi (a_{n}))^{s}$, where $\varphi$ is Euler's totient function, $s\in \mathbb{N}$, and $a_{1},\ldots, a_{N}$ are positive integers (not necessarily distinct) with some…

This paper considers the problem of approximating a Boolean function $f$ using another Boolean function from a specified class. Two classes of approximating functions are considered: $k$-juntas, and linear Boolean functions. The $n$ input…