Related papers: Explicit correlation amplifiers for finding outlie…
We prove a sensitivity-to-communication lifting theorem for arbitrary gadgets. Given functions $f: \{0,1\}^n\to \{0,1\}$ and $g : \mathcal X\times \mathcal Y\to \{0,1\}$, denote $f\circ g(x,y) := f(g(x_1,y_1),\ldots,g(x_n,y_n))$. We show…
In this paper, we leverage over-parameterization to design regularization-free algorithms for the high-dimensional single index model and provide theoretical guarantees for the induced implicit regularization phenomenon. Specifically, we…
In the Correlation Clustering problem, we are given a weighted graph $G$ with its edges labeled as "similar" or "dissimilar" by a binary classifier. The goal is to produce a clustering that minimizes the weight of "disagreements": the sum…
We give efficient deterministic algorithms for converting randomized query algorithms into deterministic ones. We first give an algorithm that takes as input a randomized $q$-query algorithm $R$ with description length $N$ and a parameter…
Anomaly detection algorithms are often thought to be limited because they don't facilitate the process of validating results performed by domain experts. In Contrast, deep learning algorithms for anomaly detection, such as autoencoders,…
Anomaly detection in time-series data is crucial for identifying faults, failures, threats, and outliers across a range of applications. Recently, deep learning techniques have been applied to this topic, but they often struggle in…
The covariance of two random variables measures the average joint deviations from their respective means. We generalise this well-known measure by replacing the means with other statistical functionals such as quantiles, expectiles, or…
Implicit samplers are algorithms for producing independent, weighted samples from multi-variate probability distributions. These are often applied in Bayesian data assimilation algorithms. We use Laplace asymptotic expansions to analyze two…
We study the parametric amplifier Hamiltonian within the framework of the Dunkl formalism. We introduce the Dunkl creation and annihilation operators and show that their quadratic combinations generate an $su(1,1)$ Lie algebra. The spectral…
The singular value decomposition (SVD) is a crucial tool in machine learning and statistical data analysis. However, it is highly susceptible to outliers in the data matrix. Existing robust SVD algorithms often sacrifice speed for…
Entanglement renormalization can be viewed as an encoding circuit for a family of approximate quantum error correcting codes. The logical information becomes progressively more well-protected against erasure errors at larger length scales.…
The unitary coupled cluster (UCC) approximation is one of the more promising wave-function ans\"atze for electronic structure calculations on quantum computers via the variational quantum eigensolver algorithm. However, for large systems…
Inference of instrumental variable regression models with many weak instruments attracts many attentions recently. To extend the classical Anderson-Rubin test to high-dimensional setting, many procedures adopt ridge-regularization. However,…
We consider a square random matrix of size N of the form A + Y where A is deterministic and Y has iid entries with variance 1/N. Under mild assumptions, as N grows, the empirical distribution of the eigenvalues of A+Y converges weakly to a…
New families of time-dependent potentials related to the parametric oscillator are introduced. This is achieved by introducing some general time-dependent operators that factorize the appropriate constant of motion (quantum invariant) of…
Rerandomization is a modern experimental design technique that repeatedly randomizes treatment assignments until covariates are deemed balanced between treatment groups. This enhances the precision and coherence of causal effect estimators,…
Derandomization techniques are often used within advanced randomized algorithms. In particular, pseudorandom objects, such as hash families and expander graphs, are key components of such algorithms, but their verification presents a…
We introduce the transcorrelated Density Matrix Renormalization Group (tcDMRG) theory for the efficient approximation of the energy for strongly correlated systems. tcDMRG encodes the wave function as a product of a fixed Jastrow or…
For two types of moderate growth representations of $(\mathbb{R}^d,+)$ on sequentially complete locally convex Hausdorff spaces (including F-representations [J. Funct. Anal. 262 (2012), 667-681], we introduce Denjoy-Carleman classes of…
In this paper, an evolutionary-based sparse regression algorithm is proposed and applied onto experimental data collected from a Duffing oscillator setup and numerical simulation data. Our purpose is to identify the Coulomb friction terms…