Related papers: Abstract embeddability ranks
We investigate natural variations of behaviourally correct learning and explanatory learning -- two learning paradigms studied in algorithmic learning theory -- that allow us to ``learn'' equivalence relations on Polish spaces. We give a…
The so-called block-term decomposition (BTD) tensor model, especially in its rank-$(L_r,L_r,1)$ version, has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of…
Clustering is widely studied in statistics and machine learning, with applications in a variety of fields. As opposed to classical algorithms which return a single clustering solution, Bayesian nonparametric models provide a posterior over…
Low rank inference on matrices is widely conducted by optimizing a cost function augmented with a penalty proportional to the nuclear norm $\Vert \cdot \Vert_*$. However, despite the assortment of computational methods for such problems,…
The alternating and non-alternating harmonic sums and other algebraic objects of the same equivalence class are connected by algebraic relations which are induced by the product of these quantities and which depend on their index class…
We study computable embeddings for pairs of structures, i.e. for classes containing precisely two non-isomorphic structures. Surprisingly, even for some pairs of simple linear orders, computable embeddings induce a non-trivial degree…
Bessel potential spaces, introduced in the 1960s, are derived through complex interpolation between Lebesgue and Sobolev spaces, making them intermediate spaces of fractional differentiability order. Bessel potential spaces have recently…
This work introduces the causal bootstrap, a framework for bounding smeared spectral observables from finite non-perturbative Euclidean data. The method optimizes over the convex set of positive spectral densities compatible with the data…
Optimal higher-order Sobolev type embeddings are shown to follow via isoperimetric inequalities. This establishes a higher-order analogue of a well-known link between first-order Sobolev embeddings and isoperimetric inequalities. Sobolev…
Understanding the structure of knowledge domains is one of the foundational challenges in science of science. Here, we propose a neural embedding technique that leverages the information contained in the citation network to obtain…
Admissible orders play a key role in ranking subintervals of the unit interval. In 2013, Bustince et al. proposed constructing such relations by means of admissible pairs of aggregation functions. The only significant example in the…
We present a new method for embedding a causal set into Minkowski spacetime. The method is similar to a previously presented method, but is simpler and provides better embedding results. The method uses spacetime volumes to define causal…
Determining a linear utility function that correlates with observed candidate rankings is a foundational problem with applications in domains such as admissions, hiring, and recommendation systems, e.g., [Storandt and Funke, AAAI'19, Zhang…
In the past few years powerful generalizations to the Euclidean k-means problem have been made, such as Bregman clustering [7], co-clustering (i.e., simultaneous clustering of rows and columns of an input matrix) [9,18], and tensor…
This paper develops a general causal inference method for treatment effects models with noisily measured confounders. The key feature is that a large set of noisy measurements are linked with the underlying latent confounders through an…
We analyze the embedding properties between Besov spaces, defined on the total space $\mathbb R^n$ and on bounded domains. We give a complete classification on whether or not these embedding maps satisfy certain weak compactness…
Ranking and comparing items is crucial for collecting information about preferences in many areas, from marketing to politics. The Mallows rank model is among the most successful approaches to analyse rank data, but its computational…
Sobolev-type embeddings on metric measure spaces encode a subtle interaction between the analytic regularity of functions and the geometry of the underlying domain space. In this paper we develop an embedding theory for variable…
This paper introduces an approach for detecting differences in the first-order structures of spatial point patterns. The proposed approach leverages the kernel mean embedding in a novel way by introducing its approximate version tailored to…
For each ordinal $\alpha<\omega_1$, we introduce the class of $\alpha$-balanced Polish groups. These classes form a hierarchy that completely stratifies the space between the class of Polish groups admitting a two-side-invariant metric…