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We study a least square-type estimator for an unknown parameter in the drift coefficient of a stochastic differential equation with additive fractional noise of Hurst parameter H>1/2. The estimator is based on discrete time observations of…
Privacy preservation has become a critical concern in high-dimensional data analysis due to the growing prevalence of data-driven applications. Since its proposal, sliced inverse regression has emerged as a widely utilized statistical…
We present a quantum algorithm for fitting a linear regression model to a given data set using the least squares approach. Different from previous algorithms which yield a quantum state encoding the optimal parameters, our algorithm outputs…
Stochastic models that predict adaptive filtering algorithms performance usually employ several assumptions in order to simplify the analysis. Although these simplifications facilitate the recursive update of the statistical quantities of…
We derive finite time error bounds for estimating general linear time-invariant (LTI) systems from a single observed trajectory using the method of least squares. We provide the first analysis of the general case when eigenvalues of the LTI…
In this work, we construct a stable and fairly fast estimator for solving non-parametric multidimensional regression problems. The proposed estimator is based on the use of multivariate Jacobi polynomials that generate a basis for a reduced…
We give the first polynomial-time algorithm to estimate the mean of a $d$-variate probability distribution with bounded covariance from $\tilde{O}(d)$ independent samples subject to pure differential privacy. Prior algorithms for this…
This paper studies the design of an optimal privacyaware estimator of a public random variable based on noisy measurements which contain private information. The public random variable carries non-private information, however, its estimate…
We introduce a statistical physics inspired supervised machine learning algorithm for classification and regression problems. The method is based on the invariances or stability of predicted results when known data is represented as…
In this paper, we present perturbation analysis and randomized algorithms for the total least squares (TLS) problems. We derive the perturbation bound and check its sharpness by numerical experiments. Motivated by the recently popular…
In this work, we show that for all statistical estimation problems, a natural MMSE instability (discontinuity) condition implies the failure of stable algorithms, serving as a version of OGP for estimation tasks. Using this criterion, we…
We consider the problem of fitting the parameters of a high-dimensional linear regression model. In the regime where the number of parameters $p$ is comparable to or exceeds the sample size $n$, a successful approach uses an…
In this paper, we consider the problem of differentially private (DP) algorithms for isotonic regression. For the most general problem of isotonic regression over a partially ordered set (poset) $\mathcal{X}$ and for any Lipschitz loss…
We present a fast, differentially private algorithm for high-dimensional covariance-aware mean estimation with nearly optimal sample complexity. Only exponential-time estimators were previously known to achieve this guarantee. Given $n$…
There are many practical applications based on the Least Square Error (LSE) approximation. It is based on a square error minimization 'on a vertical' axis. The LSE method is simple and easy also for analytical purposes. However, if data…
Ordinary Differential Equations are widespread tools to model chemical, physical, biological process but they usually rely on parameters which are of critical importance in terms of dynamic and need to be estimated directly from the data.…
We investigate a problem of finding the minimum, in which each user has a real value and we want to estimate the minimum of these values under the local differential privacy constraint. We reveal that this problem is fundamentally…
We consider stochastic differential equations (SDEs) driven by small L\'evy noise with some unknown parameters, and propose a new type of least squares estimators based on discrete samples from the SDEs. To approximate the increments of a…
We study the problem of estimating a set of $d$ linear queries with respect to some unknown distribution $\mathbf{p}$ over a domain $\mathcal{J}=[J]$ based on a sensitive data set of $n$ individuals under the constraint of local…
We give the first polynomial-time algorithm for performing linear or polynomial regression resilient to adversarial corruptions in both examples and labels. Given a sufficiently large (polynomial-size) training set drawn i.i.d. from…