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Machine learning-supported decisions, such as ordering diagnostic tests or determining preventive custody, often require converting probabilistic forecasts into binary classifications. We adopt a consequentialist perspective from decision…
We investigate computability theoretic and descriptive set theoretic contents of various kinds of analytic choice principles by performing detailed analysis of the Medvedev lattice of $\Sigma^1_1$-closed sets. Among others, we solve an open…
This paper is an extended version of our work in \cite{Ca2025}. We extend the concept of effective reducibility between statements of set theory with ordinal Turing machines (OTMs) explored in \cite{Ca2018} for $\Pi_{2}$-statements to…
We investigate infinitary wellfounded systems for linear logic with fixed points, with transfinite branching rules indexed by some closure ordinal $\alpha$ for fixed points. Our main result is that provability in the system for some…
Information-theoretic bounded rationality describes utility-optimizing decision-makers whose limited information-processing capabilities are formalized by information constraints. One of the consequences of bounded rationality is that…
We investigate the topological aspects of some algebraic computation models, in particular the BSS-model. Our results can be seen as bounds on how different BSS-computability and computability in the sense of computable analysis can be. The…
We study the equational theory of the Weihrauch lattice with multiplication, meaning the collection of equations between terms built from variables, the lattice operations $\sqcup$, $\sqcap$, the product $\times$, and the finite…
In transfer learning, we wish to make inference about a target population when we have access to data both from the distribution itself, and from a different but related source distribution. We introduce a flexible framework for transfer…
Computably enumerable equivalence relations (ceers) received a lot of attention in the literature. The standard tool to classify ceers is provided by the computable reducibility $\leq_c$. This gives rise to a rich degree-structure. In this…
We introduce an operator on problems in Weihrauch complexity, which we call the inverse limit, and which corresponds to an infinite compositional product. This operation arises naturally whenever one implements algorithms that produce a…
Reverse mathematics studies which subsystems of second order arithmetic are equivalent to key theorems of ordinary, non-set-theoretic mathematics. The main philosophical application of reverse mathematics proposed thus far is foundational…
We propose a novel framework for incorporating qualitative data into quantitative models for causal estimation. Previous methods use categorical variables derived from qualitative data to build quantitative models. However, this approach…
We define a class of computable functions over real numbers using functional schemes similar to the class of primitive and partial recursive functions defined by G\"odel and Kleene. We show that this class of functions can also be…
We develop a novel family of algorithms for the online learning setting with regret against any data sequence bounded by the empirical Rademacher complexity of that sequence. To develop a general theory of when this type of adaptive regret…
Algorithmic fairness plays an increasingly critical role in machine learning research. Several group fairness notions and algorithms have been proposed. However, the fairness guarantee of existing fair classification methods mainly depends…
Bounded rationality, that is, decision-making and planning under resource limitations, is widely regarded as an important open problem in artificial intelligence, reinforcement learning, computational neuroscience and economics. This paper…
Specifying a computational problem requires fixing encodings for input and output: encoding graphs as adjacency matrices, characters as integers, integers as bit strings, and vice versa. For such discrete data, the actual encoding is…
In this work we investigate the Weihrauch degree of the problem $\mathsf{DS}$ of finding an infinite descending sequence through a given ill-founded linear order, which is shared by the problem $\mathsf{BS}$ of finding a bad sequence…
Our capacity to process information depends on the computational power at our disposal. Information theory captures our ability to distinguish states or communicate messages when it is unconstrained with unrivaled beauty and elegance. For…
The study of the fundamental limits of information systems is a central theme in information theory. Both the traditional analytical approach and the recently proposed computational approach have significant limitations, where the former is…