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In 1981 Hong and Kung proved a lower bound on the amount of communication needed to perform dense, matrix-multiplication using the conventional $O(n^3)$ algorithm, where the input matrices were too large to fit in the small, fast memory. In…
Ordinal data are often seen in real applications. Regular multicategory classification methods are not designed for this data type and a more proper treatment is needed. We consider a framework of ordinal classification which pools the…
Madden has shown that in contrast to the situation with frames, the smallest dense quotient of a $\kappa$-frame need not be Boolean. We characterise these so-called d-reduced $\kappa$-frames as those which may be embedded as a generating…
When modeling the distribution of a multivariate continuous random vector using the so-called \emph{copula approach}, it is not uncommon to have ties in the coordinate samples of the available data because of rounding or lack of measurement…
The kernel-based method has been successfully applied in linear system identification using stable kernel designs. From a Gaussian process perspective, it automatically provides probabilistic error bounds for the identified models from the…
Machine-learning systems used in survey-based social measurement require uncertainty estimates that are reliable across population subgroups, not merely valid in aggregate. We study ordinal conformal prediction for five-level AI-attitude…
Probability density estimation from observed data constitutes a central task in statistics. In this brief, we focus on the problem of estimating the copula density associated to any observed data, as it fully describes the dependence…
The mutual information (MI) between two random variables is an important correlation measure in data analysis. The Shannon entropy of a joint probability distribution is the variable part under fixed marginals. We aim to minimize and…
We continue the investigations in the author's book on cardinal arithmetic, assuming some knowledge of it. We deal with the cofinality of (S_{<= aleph_0}(kappa), subseteq) for kappa real valued measurable (Section 3), densities of box…
We prove several results giving lower bounds for the large cardinal strength of a failure of the singular cardinal hypothesis. The main result is the following theorem: Theorem: Suppose $\kappa$ is a singular strong limit cardinal and…
We prove tight lower bounds for online multicalibration, establishing an information-theoretic separation from marginal calibration. In the general setting where group functions can depend on both context and the learner's predictions, we…
Every numerical general relativistic investigation starts from the solution of the initial value equations at a given time. Astrophysically relevant initial values for different systems lead to distinct set of equations that obey specific…
Multivariate mutual information provides a conceptual framework for characterizing higher-order interactions in complex systems. Two well-known measures of multivariate information---total correlation and dual total correlation---admit a…
We analyze the performance of the Borda counting algorithm in a non-parametric model. The algorithm needs to utilize probabilistic rankings of the items within $m$-sized subsets to accurately determine which items are the overall top-$k$…
Centered kernel alignment (CKA) is a popular metric for comparing representations, determining equivalence of networks, and neuroscience research. However, CKA does not account for the underlying manifold and relies on numerous heuristics…
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…
The canonical correlation analysis (CCA) is commonly used to analyze data sets with paired data, e.g. measurements of gene expression and metabolomic intensities of the same experiments. This allows to find interesting relationships between…
Bregman proximal point algorithm (BPPA) has witnessed emerging machine learning applications, yet its theoretical understanding has been largely unexplored. We study the computational properties of BPPA through learning linear classifiers…
Identifying cause-effect relations among variables is a key step in the decision-making process. While causal inference requires randomized experiments, researchers and policymakers are increasingly using observational studies to test…
We show that kernel-based quadrature rules for computing integrals can be seen as a special case of random feature expansions for positive definite kernels, for a particular decomposition that always exists for such kernels. We provide a…