相关论文: SQ Lower Bounds for Non-Gaussian Component Analysi…

We study the stochastic optimization of canonical correlation analysis (CCA), whose objective is nonconvex and does not decouple over training samples. Although several stochastic gradient based optimization algorithms have been recently…

Automating statistical modelling is a challenging problem in artificial intelligence. The Automatic Statistician takes a first step in this direction, by employing a kernel search algorithm with Gaussian Processes (GP) to provide…

An instance of a group testing problem is a set of objects $\cO$ and an unknown subset $P$ of $\cO$. The task is to determine $P$ by using queries of the type ``does $P$ intersect $Q$'', where $Q$ is a subset of $\cO$. This problem occurs…

The quantum approximate optimization algorithm (QAOA) is a method of approximately solving combinatorial optimization problems. While QAOA is developed to solve a broad class of combinatorial optimization problems, it is not clear which…

We consider the problem of principal component analysis (PCA) in a streaming stochastic setting, where our goal is to find a direction of approximate maximal variance, based on a stream of i.i.d. data points in $\reals^d$. A simple and…

We study nonclassical correlations beyond entanglement in a family of two-mode non-Gaussian states which represent the continuous-variable counterpart of two-qubit Werner states. We evaluate quantum discord and other quantumness measures…

We use techniques for lower bounds on communication to derive necessary conditions in terms of detector efficiency or amount of super-luminal communication for being able to reproduce with classical local hidden-variable theories the…

We prove that $\tilde{\Theta}(k d^2 / \varepsilon^2)$ samples are necessary and sufficient for learning a mixture of $k$ Gaussians in $\mathbb{R}^d$, up to error $\varepsilon$ in total variation distance. This improves both the known upper…

Principal Component Analysis (PCA) is a cornerstone of dimensionality reduction, yet its classical formulation relies critically on second-order moments and is therefore fragile in the presence of heavy-tailed data and impulsive noise.…

The quantum approximate optimization algorithm, also known in its generalization as the quantum alternating operator ansatz, (QAOA) is a heuristic hybrid quantum-classical algorithm for finding high-quality approximate solutions to…

Gaussian mixtures are a powerful and widely used tool to model non-Gaussian estimation problems. They are able to describe measurement errors that follow arbitrary distributions and can represent ambiguity in assignment tasks like point set…

This paper concerns quasi-stochastic approximation (QSA) to solve root finding problems commonly found in applications to optimization and reinforcement learning. The general constant gain algorithm may be expressed as the…

Dimensionality reduction is a crucial step for pattern recognition and data mining tasks to overcome the curse of dimensionality. Principal component analysis (PCA) is a traditional technique for unsupervised dimensionality reduction, which…

The thermal-equilibrium canonical distribution is currently obtained by maximizing the Boltzmann-Gibbs-von Neumann-Shannon entropy $S_{BG}(p)=k\sum^{W}_{i=1}p_{i}\ln 1/p_{i}$ constrained to $\sum^{W}_{i=1}p_{i}=1$ and…

We present upper and lower bounds for the prediction error of the Lasso. For the case of random Gaussian design, we show that under mild conditions the prediction error of the Lasso is up to smaller order terms dominated by the prediction…

In adaptive data analysis, the user makes a sequence of queries on the data, where at each step the choice of query may depend on the results in previous steps. The releases are often randomized in order to reduce overfitting for such…

This article establishes a new and comprehensive estimation and inference theory for principal component analysis (PCA) under the weak factor model that allow for cross-sectional dependent idiosyncratic components under the nearly minimal…

We introduce a simple diagnostic test for assessing the overall or partial goodness of fit of a linear causal model with errors being independent of the covariates. In particular, we consider situations where hidden confounding is…

We report the first improvement in the space-time trade-off of lower bounds for the orthogonal range searching problem in the semigroup model, since Chazelle's result from 1990. This is one of the very fundamental problems in range…

In this paper, we develop machinery which makes it much easier to prove sum of squares lower bounds when the problem is symmetric under permutations of $[1,n]$ and the unsatisfiability of our problem comes from integrality arguments, i.e.…