相关论文: Strong Data Processing Inequalities and their Appl…

Variable selection in ultra-high dimensional regression problems has become an important issue. In such situations, penalized regression models may face computational problems and some pre screening of the variables may be necessary. A…

Many of the traditional results in information theory, such as the channel coding theorem or the source coding theorem, are restricted to scenarios where the underlying resources are independent and identically distributed (i.i.d.) over a…

We provide a novel upper-bound on Witsenhausen's rate, the rate required in the zero-error analogue of the Slepian-Wolf problem; our bound is given in terms of a new information-theoretic functional defined on a certain graph. We then use…

In order to formally understand the power of neural computing, we first need to crack the frontier of threshold circuits with two and three layers, a regime that has been surprisingly intractable to analyze. We prove the first super-linear…

We study the statistical performance of semidefinite programming (SDP) relaxations for clustering under random graph models. Under the $\mathbb{Z}_{2}$ Synchronization model, Censored Block Model and Stochastic Block Model, we show that SDP…

The non-convexity and intractability of distributionally robust chance constraints make them challenging to cope with. From a data-driven perspective, we propose formulating it as a robust optimization problem to ensure that the…

We present experimental work on a primal-dual framework simultaneously approximating maximum cut and weighted fractional cut-covering instances. In this primal-dual framework, we solve a semidefinite programming (SDP) relaxation to either…

In this paper, we consider the problem of partitioning a small data sample of size $n$ drawn from a mixture of 2 sub-gaussian distributions in $\R^p$. We consider semidefinite programming relaxations of an integer quadratic program that is…

Determining the optimal fidelity for the transmission of quantum information over noisy quantum channels is one of the central problems in quantum information theory. Recently, [Berta-Borderi-Fawzi-Scholz, Mathematical Programming, 2021]…

Recent advances in Symmetric Positive Definite (SPD) matrix learning show that Riemannian metrics are fundamental to effective SPD neural networks. Motivated by this, we revisit the geometry of the Cholesky factors and uncover a simple…

An arbitrarily reliable quantum computer can be efficiently constructed from noisy components using a recursive simulation procedure, provided that those components fail with probability less than the fault-tolerance threshold. Recent…

Motivated by the recent experimental demonstrations of quantum supremacy, proving the hardness of the output of random quantum circuits is an imperative near term goal. We prove under the complexity theoretical assumption of the…

We derive an exact and efficient Bayesian regression algorithm for piecewise constant functions of unknown segment number, boundary location, and levels. It works for any noise and segment level prior, e.g. Cauchy which can handle outliers.…

Fault detection and identification (FDI) is critical for maintaining the safety and reliability of systems subject to actuator and sensor faults. In this paper, the problem of FDI for nonlinear control-affine systems under simultaneous…

A notorious open question in circuit complexity is whether Boolean operations of arbitrary arity can efficiently be expressed using modular counting gates only. H{\aa}stad's celebrated switching lemma yields exponential lower bounds for the…

The new field of adaptive data analysis seeks to provide algorithms and provable guarantees for models of machine learning that allow researchers to reuse their data, which normally falls outside of the usual statistical paradigm of static…

Modern computing systems based on the von Neumann architecture are built from silicon complementary metal oxide semiconductor (CMOS) transistors that need to operate under practically error free conditions with 1 error in $10^{15}$…

We study the fundamental problem of high-dimensional mean estimation in a robust model where a constant fraction of the samples are adversarially corrupted. Recent work gave the first polynomial time algorithms for this problem with…

Let $\mathsf{TH}_k$ denote the $k$-out-of-$n$ threshold function: given $n$ input Boolean variables, the output is $1$ if and only if at least $k$ of the inputs are $1$. We consider the problem of computing the $\mathsf{TH}_k$ function…

Many differentially private (DP) data release systems either output DP synthetic data and leave analysts to perform inference as usual, which can lead to severe miscalibration, or output a DP point estimate without a principled way to do…