arXiv research

SOEM clusters time series data with improved accuracy.

We give a short elementary proof that a Khovanov-type link homology constructed from a diagonalisable Frobenius algebra is degenerate.

Geodesic flows with diagonalisable integrals are orthogonal.

The paper constrains families of smooth 4-manifolds using Seiberg-Witten invariants.

Penrose limit results for specific 3-surfaces in space-time.

Extends method for solving certain hydrodynamic systems.

Smooth but not symplectic embeddings of rational balls in complex projective plane found.

The paper studies symmetries and conservation laws of non-diagonalisable hydrodynamic systems.

We wish to attack the problems that H.~Anciaux and K.~Panagiotidou posed in [1], for non-degenerate real hypersurfaces in indefinite complex projective space. We will slightly change these authors' point of view, obtaining cleaner equations for the almost contact metric structure. To make the theory meaningful, we cons…

We prove that for an algebraic curvature tensor on a pseudo-Euclidean space, the Jordan-Osserman condition implies the Rakić duality principle, and that the Osserman condition and the duality principle are equivalent in the diagonalisable case.

Diagonalizes tautological classes of definite 4-manifolds.

We generalise theorems of Cochran-Lickorish and Owens-Strle to the case of links with more than one component. This enables the use of linking forms on double branched covers, Heegaard Floer correction terms, and Donaldson's diagonalisation theorem to complete the table of unlinking numbers for nonsplit prime links wit…

We consider the problem of approximate joint triangularization of a set of noisy jointly diagonalizable real matrices. Approximate joint triangularizers are commonly used in the estimation of the joint eigenstructure of a set of matrices, with applications in signal processing, linear algebra, and tensor decomposition.…

Unified theorem for deep and shallow joint-equivariant machines.

This is the second of a series of papers dealing with an analog in Arakelov geometry of the holomorphic Lefschetz fixed point formula. We use the main result of the first paper to prove a residue formula "`a la Bott" for arithmetic characteristic classes living on arithmetic varieties acted upon by a diagonalisable tor…

New integrable systems constructed for non-diagonal Killing tensors.

It is shown that, in four dimensions, it is possible to introduce coordinates so that an analytic metric locally takes block diagonal form. i.e. one can find coordinates such that $g_{αβ} = 0$ for $(α, β) \in S$ where $S = {(1, 3), (1, 4), (2, 3), (2, 4)}$. We call a coordinate system in which the metric takes this for…

Improved multimodal variational models capture more complex joint distributions.

We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data. In particular, we write the joint density approximately as a product of an approximate posterior dens…

Study approximates top Lyapunov exponents for surface mapping classes.

Paper explores supervised learning methods to approximate ideal observer for joint signal detection and localization.

Novel approach for estimating joint probability densities using tensor decompositions and dictionaries.

New method uses joint stochastic approximation to improve learning of discrete latent models.

Due to the intractable partition function, the exact likelihood function for a Markov random field (MRF), in many situations, can only be approximated. Major approximation approaches include pseudolikelihood and Laplace approximation. In this paper, we propose a novel way of approximating the likelihood function throug…

Study proposes a new model for joint survival annuity valuation.

Research in several fields now requires the analysis of data sets in which multiple high-dimensional types of data are available for a common set of objects. In particular, The Cancer Genome Atlas (TCGA) includes data from several diverse genomic technologies on the same cancerous tumor samples. In this paper we introd…

The paper emphasizes the importance of joint predictions over marginal predictions for decision-making.

In his 2011 work, Maas has shown that the law of any time-reversible continuous-time Markov chain with finite state space evolves like a gradient flow of the relative entropy with respect to its stationary distribution. In this work we show the converse to the above by showing that if the relative law of a Markov chain…

Markov networks are extensively used to model complex sequential, spatial, and relational interactions in a wide range of fields. By learning the structure of independences of a domain, more accurate joint probability distributions can be obtained for inference tasks or, more directly, for interpreting the most signifi…

New methods improve Bayesian inference and decision-making in online learning.

Paper develops a theory explaining contrastive pre-training for multimodal AI.

This letter extends the concept of graph-frequency to graph signals that evolve with time. Our goal is to generalize and, in fact, unify the familiar concepts from time- and graph-frequency analysis. To this end, we study a joint temporal and graph Fourier transform (JFT) and demonstrate its attractive properties. We b…

Study improves probabilistic circuits using transformations for better predictions.

New research suggests continual learning should focus on both optimization objective and optimization trajectory.

The most direct way to express arbitrary dependencies in datasets is to estimate the joint distribution and to apply afterwards the argmax-function to obtain the mode of the corresponding conditional distribution. This method is in practice difficult, because it requires a global optimization of a complicated function,…

There has recently been considerable interest in completing a low-rank matrix or tensor given only a small fraction (or few linear combinations) of its entries. Related approaches have found considerable success in the area of recommender systems, under machine learning. From a statistical estimation point of view, the…

Framework for systemic risk modeling using jointly exchangeable arrays.

We present a novel approximate graph matching algorithm that incorporates seeded data into the graph matching paradigm. Our Joint Optimization of Fidelity and Commensurability (JOFC) algorithm embeds two graphs into a common Euclidean space where the matching inference task can be performed. Through real and simulated …

ProJIVE integrates multiple data types to explain joint and individual variation.

The paper proposes a method to estimate joint probability from unpaired data using entropic transport kernels.

Optimizes data acquisition in high-dimensional Bayesian optimization.

The slicing number of a knot, $u_s(K)$, is the minimum number of crossing changes required to convert $K$ to a slice knot. This invariant is bounded above by the unknotting number and below by the slice genus $g_s(K)$. We show that for many knots, previous bounds on unknotting number obtained by Ozsvath and Szabo and b…

Estimates multiple related causal graphs with shared causal order.

Algorithm finds ribbon disks for alternating knots, resolving sliceness for most prime knots.

We provide a partial classification of the 3-strand pretzel knots $K = P(p,q,r)$ with unknotting number one. Following the classification by Kobayashi and Scharlemann-Thompson for all parameters odd, we treat the remaining families with $r$ even. We discover that there are only four possible subfamilies which may satis…

We formalize the problem of learning interdomain correspondences in the absence of paired data as Bayesian inference in a latent variable model (LVM), where one seeks the underlying hidden representations of entities from one domain as entities from the other domain. First, we introduce implicit latent variable models,…

This paper introduces a neural operator for probabilistic conditioning.

The approximate joint diagonalization of a set of matrices consists in finding a basis in which these matrices are as diagonal as possible. This problem naturally appears in several statistical learning tasks such as blind signal separation. We consider the diagonalization criterion studied in a seminal paper by Pham (…