Related papers: The Combinatorics of Falsification and Hypothesis …
Persistent homology is a popular tool in Topological Data Analysis. It provides numerical characteristics of data sets which reflect global geometric properties. In order to be useful in practice, for example for feature generation in…
Probability measures by themselves, are known to be inappropriate for modeling the dynamics of plain belief and their excessively strong measurability constraints make them unsuitable for some representational tasks, e.g. in the context of…
Over the years a number of topologies for the set of laws of stochastic processes have been proposed. Building on the weak topology they all aim to capture more accurately the temporal structure of the processes. In a parallel paper we show…
Ratios of universal enumerable semimeasures corresponding to hypotheses are investigated as a solution for statistical composite hypotheses testing if an unbounded amount of computation time can be assumed. Influence testing for discrete…
In this work we provide a review of basic ideas and novel developments about Conformal Prediction -- an innovative distribution-free, non-parametric forecasting method, based on minimal assumptions -- that is able to yield in a very…
In various application fields, such as fluid-, cell-, or crowd-simulations, spatial data structures are very important. They answer nearest neighbor queries which are instrumental in performing necessary computations for, e.g., taking the…
Probabilistic models based on continuous latent spaces, such as variational autoencoders, can be understood as uncountable mixture models where components depend continuously on the latent code. They have proven to be expressive tools for…
While statistics focusses on hypothesis testing and on estimating (properties of) the true sampling distribution, in machine learning the performance of learning algorithms on future data is the primary issue. In this paper we bridge the…
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…
We discuss a general approach to handling "multiple hypotheses" testing in the case when a particular hypothesis states that the vector of parameters identifying the distribution of observations belongs to a convex compact set associated…
Conformal prediction is a distribution-free technique for establishing valid prediction intervals. Although conventionally people conduct conformal prediction in the output space, this is not the only possibility. In this paper, we propose…
A hypothesis class admits a sample compression scheme, if for every sample labeled by a hypothesis from the class, it is possible to retain only a small subsample, using which the labels on the entire sample can be inferred. The size of the…
The purpose of testing a system with respect to a requirement is to refute the hypothesis that the system satisfies the requirement. We build a theory of tests and refutation based on the elementary notions of satisfaction and refinement.…
Modeling the spread of social contagions is central to various applications in social computing. In this paper, we study the learnability of the competitive threshold model from a theoretical perspective. We demonstrate how competitive…
The combination of persistent homology and discrete Morse theory has proven very effective in visualizing and analyzing big and heterogeneous data. Indeed, topology provides computable and coarse summaries of data independently from…
Agentic theorem provers combine a reasoning model, retrieval, search, and a proof assistant verifier, yet it remains unclear which components actually improve finite-budget proof success and why they help on real mathematical workloads. We…
Deep neural networks often produce miscalibrated probability estimates, leading to overconfident predictions. A common approach for calibration is fitting a post-hoc calibration map on unseen validation data that transforms predicted…
Bottom-up knowledge compilation is a paradigm for generating representations of functions by iteratively conjoining constraints using a so-called apply function. When the input is not efficiently compilable into a language - generally a…
In this paper we consider a fragment of the first-order theory of the real numbers that includes systems of equations of continuous functions in bounded domains, and for which all functions are computable in the sense that it is possible to…
$P$-values that are derived from continuously distributed test statistics are typically uniformly distributed on $(0,1)$ under least favorable parameter configurations (LFCs) in the null hypothesis. Conservativeness of a $p$-value $P$…