Related papers: A note about the generalisation of the C-tests
A measure for the complexity of a differentiable function f(x) on an interval is introduced. It is based on approximations of the function by piecewise constant functions. The measure takes into account the quality of the approximation and…
The aim of this paper is to propose an alternative behavioural definition of computation (and of a computer) based simply on whether a system is capable of reacting to the environment-the input-as reflected in a measure of programmability.…
Evaluating difficulty and biases in machine learning models has become of extreme importance as current models are now being applied in real-world situations. In this paper we present a simple method for calculating a difficulty score based…
A weighted automaton is functional if any two accepting runs on the same finite word have the same value. In this paper, we investigate functional weighted automata for four different measures: the sum, the mean, the discounted sum of…
The ability to estimate task difficulty is critical for many real-world decisions such as setting appropriate goals for ourselves or appreciating others' accomplishments. Here we give a computational account of how humans judge the…
We are given a set of elements in a metric space. The distribution of the elements is arbitrary, possibly adversarial. Can we weigh the elements in a way that is resistant to such (adversarial) manipulations? This problem arises in various…
Natural language is compositional; the meaning of a sentence is a function of the meaning of its parts. This property allows humans to create and interpret novel sentences, generalizing robustly outside their prior experience. Neural…
We prove a complexity dichotomy theorem for all non-negative weighted counting Constraint Satisfaction Problems (CSP). This caps a long series of important results on counting problems including unweighted and weighted graph homomorphisms…
Generalized equations are problems emerging in contexts of modern variational analysis as an adequate formalism to treat such issues as constraint systems, optimality and equilibrium conditions, variational inequalities, differential…
Average-case analysis computes the complexity of an algorithm averaged over all possible inputs. Compared to worst-case analysis, it is more representative of the typical behavior of an algorithm, but remains largely unexplored in…
We study the computational complexity of a robust version of the problem of testing two univariate C-finite functions for eventual inequality at large times. Specifically, working in the bit-model of real computation, we consider the…
We analyse the complexity of environments according to the policies that need to be used to achieve high performance. The performance results for a population of policies leads to a distribution that is examined in terms of policy…
We give a complexity dichotomy theorem for the counting Constraint Satisfaction Problem (#CSP in short) with complex weights. To this end, we give three conditions for its tractability. Let F be any finite set of complex-valued functions,…
Understanding generalization in deep learning is arguably one of the most important questions in deep learning. Deep learning has been successfully adopted to a large number of problems ranging from pattern recognition to complex decision…
We simplify the proof of some widely used theoretical theorems, extending their applicability, while correcting some erroneous results. We also generalize key results and present new results that contribute to the development of the theory.…
A general and relatively simple method for construction of multivariate goodness-of-fit tests is introduced. The proposed test is applied to elliptical distributions. The method is based on a characterization of probability distributions…
Although recent works have brought some insights into the performance improvement of techniques used in state-of-the-art deep-learning models, more work is needed to understand their generalization properties. We shed light on this matter…
Clustering analysis of functional data, which comprises observations that evolve continuously over time or space, has gained increasing attention across various scientific disciplines. Practical applications often involve functional data…
Genome-wide association analysis has generated much discussion about how to preserve power to detect signals despite the detrimental effect of multiple testing on power. We develop a weighted multiple testing procedure that facilitates the…
Virtually all machine learning tasks are characterized using some form of loss function, and "good performance" is typically stated in terms of a sufficiently small average loss, taken over the random draw of test data. While optimizing for…