Related papers: A Convex Analysis Approach to Computational Entrop…
Quantum random sampling is the leading proposal for demonstrating a computational advantage of quantum computers over classical computers. Recently, first large-scale implementations of quantum random sampling have arguably surpassed the…
Compression of documents, images, audios and videos have been traditionally practiced to increase the efficiency of data storage and transfer. However, in order to process or carry out any analytical computations, decompression has become…
Classification is a machine learning method used in many practical applications: text mining, handwritten character recognition, face recognition, pattern classification, scene labeling, computer vision, natural langage processing. A…
A critical question for the field of quantum computing in the near future is whether quantum devices without error correction can perform a well-defined computational task beyond the capabilities of state-of-the-art classical computers,…
We study the design of computationally efficient algorithms with provable guarantees, that are robust to adversarial (test time) perturbations. While there has been an proliferation of recent work on this topic due to its connections to…
Optimization problems in engineering and applied mathematics are typically solved in an iterative fashion, by systematically adjusting the variables of interest until an adequate solution is found. The iterative algorithms that govern these…
Pseudoentropy characterizations provide a quantitatively precise demonstration of the close relationship between computational hardness and computational randomness. We prove a unified pseudoentropy characterization that generalizes and…
This paper investigates the relation between sequential convex programming (SCP) as, e.g., defined in [24] and DC (difference of two convex functions) programming. We first present an SCP algorithm for solving nonlinear optimization…
Complex systems are characterised by a tight, nontrivial interplay of their constituents, which gives rise to a multi-scale spectrum of emergent properties. In this scenario, it is practically and conceptually difficult to identify those…
We devise a hierarchy of computational algorithms to enumerate the microstates of a system comprising N independent, distinguishable particles. An important challenge is to cope with integers that increase exponentially with system size,…
Various strategies for active learning have been proposed in the machine learning literature. In uncertainty sampling, which is among the most popular approaches, the active learner sequentially queries the label of those instances for…
To calculate the entropy of a subalgebra or of a channel with respect to a state, one has to solve an intriguing optimalization problem. The latter is also the key part in the entanglement of formation concept, in which case the subalgebra…
With the increasing deployment of machine learning systems in practice, transparency and explainability have become serious issues. Contrastive explanations are considered to be useful and intuitive, in particular when it comes to…
Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…
In this paper, we consider robust control using randomized algorithms. We extend the existing order statistics distribution theory to the general case in which the distribution of population is not assumed to be continuous and the order…
In this paper, we consider convex stochastic optimization problems arising in machine learning applications (e.g., risk minimization) and mathematical statistics (e.g., maximum likelihood estimation). There are two main approaches to solve…
Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…
We analyze the computational aspects of detecting topological order in a quantum many-body system. We contrast the widely used topological entanglement entropy with a recently introduced operational definition for topological order based on…
Certified randomness guaranteed to be unpredictable by adversaries is central to information security. The fundamental randomness inherent in quantum physics makes certification possible from devices that are only weakly characterised, i.e.…
The method of maximum entropy has been very successful but there are cases where it has either failed or led to paradoxes that have cast doubt on its general legitimacy. My more optimistic assessment is that such failures and paradoxes…