Related papers: Uniform Unfolding and Analytic Measurability
We consider strong law of large numbers (SLLN) in the framework of game-theoretic probability of Shafer and Vovk (2001). We prove several versions of SLLN for the case that Reality's moves are unbounded. Our game-theoretic versions of SLLN…
This preliminary report addresses the expressive power of unit resolution regarding input data encoded with partial truth assignments of propositional variables. A characterization of the functions that are computable in this way, which we…
In various models of set theory, we consider covering Aleph_1 x Aleph_1 rectangles by countably many smooth curves, and we study differentiable isomorphisms between Aleph_1-dense sets of reals.
Let $\mathcal{E}$ denote the space of entire functions with the topology of uniform convergence on compact sets. The action of $\mathbb C$ by translations on $\mathcal E$ is defined by $T_zf(w) = f(w+z)$. Let $\mathcal{U}$ denote the set of…
We define and study obvious strategy-proofness with respect to a partition of the set of agents. It encompasses strategy-proofness as a special case when the partition is the coarsest one and obvious strategy-proofness when the partition is…
Selective rationalization has become a common mechanism to ensure that predictive models reveal how they use any available features. The selection may be soft or hard, and identifies a subset of input features relevant for prediction. The…
When a machine learning model is deployed, its predictions can alter its environment, as better informed agents strategize to suit their own interests. With such alterations in mind, existing approaches to uncertainty quantification break.…
A relatively new topic in computability theory is the study of notions of computation that are robust against mistakes on some kind of small set. However, despite the recent popularity of this topic relatively foundational questions about…
The presence of artificial intelligence (AI) in our society is increasing, which brings with it the need to understand the behavior of AI mechanisms, including machine learning predictive algorithms fed with tabular data, text or images,…
Regular functions from infinite words to infinite words can be equivalently specified by MSO-transducers, streaming $\omega$-string transducers as well as deterministic two-way transducers with look-ahead. In their one-way restriction, the…
In this paper we provide sufficient conditions that ensure the monotonicity, respectively the global injectivity of an operator. Further, some new analytical conditions that assure the injectivity/univalence of a complex function of one…
Recent innovations from machine learning allow for data unfolding, without binning and including correlations across many dimensions. We describe a set of known, upgraded, and new methods for ML-based unfolding. The performance of these…
In a 1977 paper, Steffens identified an elegant criterion for determining when a countable graph has a perfect matching. In this paper, we will investigate the proof-theoretic strength of this result and related theorems. We show that a…
Many popular algorithmic fairness measures depend on the joint distribution of predictions, outcomes, and a sensitive feature like race or gender. These measures are sensitive to distribution shift: a predictor which is trained to satisfy…
A compression function is a map that slims down an observational set into a subset of reduced size, while preserving its informational content. In multiple applications, the condition that one new observation makes the compressed set change…
We present formalized proofs verifying that the first-order unification algorithm defined over lists of satisfiable constraints generates a most general unifier (MGU), which also happens to be idempotent. All of our proofs have been…
We show that for a Suslin ccc forcing notion $\mathbb Q$ adding a Hechler real, ``$\text{ZF}+\text{DC}_{\omega_1}+$all sets of reals are $I_{\mathbb Q,\aleph_0}$-measurable'' implies the existence of an inner model with a measurable…
We work in set-theory without choice ZF. Denoting by AC(N) the countable axiom of choice, we show in ZF+AC(N) that the closed unit ball of a uniformly convex Banach space is compact in the convex topology (an alternative to the weak…
All constructive methods employed in modern mathematics produce only countable sets, even when designed to transcend countability. We show that any constructive argument for uncountability -- excluding diagonalization techniques --…
Motivated by the goal of forecasting public sentiments, we consider a forecasting problem in the context of the Mean Field Games theory. We develop a numerical method, which is a version of the so-called convexification method. We provide…