相关论文: Algorithm and proof as \Omega-invariance and trans…

Computation models such as circuits describe sequences of computation steps that are carried out one after the other. In other words, algorithm design is traditionally subject to the restriction imposed by a fixed causal order. We address a…

We introduce a neural network architecture to solve inverse problems linked to a one-dimensional integral operator. This architecture is built by unfolding a forward-backward algorithm derived from the minimization of an objective function…

Orthogonal Monte Carlo (OMC) is a very effective sampling algorithm imposing structural geometric conditions (orthogonality) on samples for variance reduction. Due to its simplicity and superior performance as compared to its Quasi Monte…

Design-based simulations - procedures that hold realized outcomes fixed and generate variation by resampling treatment assignment or shocks - are widely used in both methodological and applied work to assess inference procedures. This paper…

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 give an overview over the usefulness of the concept of equivariance and invariance in the design of experiments for generalized linear models. In contrast to linear models here pairs of transformations have to be considered which act…

Probability intervals are an attractive tool for reasoning under uncertainty. Unlike belief functions, though, they lack a natural probability transformation to be used for decision making in a utility theory framework. In this paper we…

We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…

We introduce a new method for estimating the parameter of the bivariate Clayton copulas within the framework of Algorithmic Inference. The method consists of a variant of the standard boot-strapping procedure for inferring random…

A structural analysis of construction schemes is developed. That analysis is used to give simple and new constructions of combinatorial objects which have been of interest to set theorists and topologists. We then continue the study of…

A general conversion strategy by involving a shifted parameter $\theta$ is proposed to construct high-order accuracy difference formulas for fractional calculus operators. By converting the second-order backward difference formula with such…

In inference problems involving a multi-dimensional parameter $\theta$, it is often natural to consider decision rules that have a risk which is invariant under some group $G$ of permutations of $\theta$. We show that this implies that the…

Algorithms are ways of mapping problems to solutions. An algorithm is invertible precisely when this mapping is injective, such that the initial problem can be uniquely inferred from its solution. While invertible algorithms can be…

Inductive proofs can be represented as proof schemata, i.e. as parameterized sequences of proofs defined in a primitive recursive way. Applications of proof schemata can be found in the area of automated proof analysis where the schemata…

Algorithm extraction aims to synthesize executable programs directly from models trained on algorithmic tasks, enabling de novo algorithm discovery without relying on human-written code. However, applying this paradigm to Transformer is…

Mechanical systems are often characterized only by their response to certain loads known from experiments or simulations. The obtained data can be used for various purposes: system analysis, design of mathematical models, or construction of…

Ordinal measurements are common outcomes in studies within psychology, as well as in the social and behavioral sciences. Choosing an appropriate regression model for analysing such data poses a difficult task. This paper aims to facilitate…

We introduce a framework uniting algorithmic randomness with exchangeable credences to address foundational questions in philosophy of probability and philosophy of science. To demonstrate its power, we show how one might use the framework…

Recurrence equations have played a central role in static cost analysis, where they can be viewed as abstractions of programs and used to infer resource usage information without actually running the programs with concrete data. Such…

Transfer learning, also referred as knowledge transfer, aims at reusing knowledge from a source dataset to a similar target one. While many empirical studies illustrate the benefits of transfer learning, few theoretical results are…