相关论文: Hardness of sampling solutions from the Symmetric …
We consider the sample complexity of learning with adversarial robustness. Most prior theoretical results for this problem have considered a setting where different classes in the data are close together or overlapping. Motivated by some…
Statistical tasks such as density estimation and approximate Bayesian inference often involve densities with unknown normalising constants. Score-based methods, including score matching, are popular techniques as they are free of…
In this work, we examine sampling problems with non-smooth potentials. We propose a novel Markov chain Monte Carlo algorithm for sampling from non-smooth potentials. We provide a non-asymptotical analysis of our algorithm and establish a…
We are interested in the problem of robust parametric estimation of a density from $n$ i.i.d. observations. By using a practice-oriented procedure based on robust tests, we build an estimator for which we establish non-asymptotic risk…
Binary code similarity detection is a core task in reverse engineering. It supports malware analysis and vulnerability discovery by identifying semantically similar code in different contexts. Modern methods have progressed from manually…
We consider active learning for binary classification in the agnostic pool-based setting. The vast majority of works in active learning in the agnostic setting are inspired by the CAL algorithm where each query is uniformly sampled from the…
In many instances, the application of approximate Bayesian methods is hampered by two practical features: 1) the requirement to project the data down to low-dimensional summary, including the choice of this projection, which ultimately…
We study the computational complexity of two Boolean nonlinearity measures: the nonlinearity and the multiplicative complexity. We show that if one-way functions exist, no algorithm can compute the multiplicative complexity in time…
Two commonly arising computational tasks in Bayesian learning are Optimization (Maximum A Posteriori estimation) and Sampling (from the posterior distribution). In the convex case these two problems are efficiently reducible to each other.…
We consider the hardness of approximation of optimization problems from the point of view of definability. For many NP-hard optimization problems it is known that, unless P = NP, no polynomial-time algorithm can give an approximate solution…
The problem of 1-bit compressive sampling is addressed in this paper. We introduce an optimization model for reconstruction of sparse signals from 1-bit measurements. The model targets a solution that has the least l0-norm among all signals…
We devise a deterministic algorithm to efficiently sample high-quality solutions of certain spin-glass systems that encode hard optimization problems. We employ tensor networks to represent the Gibbs distribution of all possible…
We consider global optimization problems, where the feasible region $\X$ is a compact subset of $\mathbb{R}^d$ with $d \geq 10$. For these problems, we demonstrate the following. First: the actual convergence of global random search…
We give a $2^{\tilde{O}(\sqrt{n}/\epsilon)}$-time algorithm for properly learning monotone Boolean functions under the uniform distribution over $\{0,1\}^n$. Our algorithm is robust to adversarial label noise and has a running time nearly…
We characterize the power of constant-depth Boolean circuits in generating uniform symmetric distributions. Let $f\colon\{0,1\}^m\to\{0,1\}^n$ be a Boolean function where each output bit of $f$ depends only on $O(1)$ input bits. Assume the…
BosonSampling is a quantum mechanical task involving Fock basis state preparation and detection and evolution using only linear interactions. A classical algorithm for producing samples from this quantum task cannot be efficient unless the…
Current techniques in machine learning are so far are unable to learn classifiers that are robust to adversarial perturbations. However, they are able to learn non-robust classifiers with very high accuracy, even in the presence of random…
We study the problem of learning general (i.e., not necessarily homogeneous) halfspaces with Random Classification Noise under the Gaussian distribution. We establish nearly-matching algorithmic and Statistical Query (SQ) lower bound…
Simulating quantum circuits using classical computers lets us analyse the inner workings of quantum algorithms. The most complete type of simulation, strong simulation, is believed to be generally inefficient. Nevertheless, several…
Randomized algorithms depend on accurate sampling from probability distributions, as their correctness and performance hinge on the quality of the generated samples. However, even for common distributions like Binomial, exact sampling is…