A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Circle graph complexes reveal link properties via Khovanov homology.
We study the sample complexity of learning neural networks, by providing new bounds on their Rademacher complexity assuming norm constraints on the parameter matrix of each layer. Compared to previous work, these complexity bounds have improved dependence on the network depth, and under some additional assumptions, are…
GTMs model complex multivariate data with varying conditional independencies.
New algorithms test independence with fewer samples by using predictive information.
Study on complex line fields on almost-complex manifolds, proving existence conditions.
Representing distributions over permutations can be a daunting task due to the fact that the number of permutations of objects scales factorially in . One recent way that has been used to reduce storage complexity has been to exploit probabilistic independence, but as we argue, full independence assumptions impo…
New algorithm reduces conditional independence tests needed for causal discovery.
Proves a conjecture about graph complexes without specific cycle lengths.
Improved sample complexity for ReLU networks with norm constraints.
Paper solves a metric-independent problem on almost Kähler 4-manifolds.
Study shows priors are crucial for accurate causal learning from unlabeled data.
Paper discovers simplicial complexes connecting trained models for improved ensembling.
E-CIT framework reduces CITs' computational burden and improves causal discovery performance.
Testing for conditional independence is a core aspect of constraint-based causal discovery. Although commonly used tests are perfect in theory, they often fail to reject independence in practice, especially when conditioning on multiple variables. We focus on discrete data and propose a new test based on the notion of …
Optimal transport is #P-hard when components are independent, even with approximate solutions.
New test detects independence in streaming data, adapting to data complexity.
Study shows -NN regressor consistency in complex survey designs.
A new method tests conditional independence by transforming it into an unconditional problem using transport maps.
New algorithms for RL in Markov games with independent linear function approximation, breaking the curse of multiagents.
We define analytic torsion of Z_2-graded elliptic complexes as an element in the graded determinant line of the cohomology of the complex, generalizing most of the variants of Ray-Singer analytic torsion in the literature. It applies to a myriad of new examples, including flat superconnection complexes, twisted analyti…
Extends VAEs to handle complex Bayesian network structures.
This paper explores Khovanov adequacy in knot theory.
Closed-form formulas for path-independent options in a specific Lévy model.
New algorithm learns halfspaces with noise using Forster decomposition.
Inferring the causal structure that links n observables is usually based upon detecting statistical dependences and choosing simple graphs that make the joint measure Markovian. Here we argue why causal inference is also possible when only single observations are present. We develop a theory how to generate causal grap…
In the last two decades, unsupervised latent variable models---blind source separation (BSS) especially---have enjoyed a strong reputation for the interpretable features they produce. Seldom do these models combine the rich diversity of information available in multiple datasets. Multidatasets, on the other hand, yield…
Let M be a K3 surface or an even-dimensional compact torus. We show that the category of coherent sheaves on M is independent from the choice of the complex structure, if this complex structure is generic.
We study the wealth distribution of the Bouchaud--Mézard (BM) model on complex networks. It has been known that this distribution depends on the topology of network by numerical simulations, however, no one have succeeded to explain it. Using "adiabatic" and "independent" assumptions along with the central-limit theore…
Unified framework for structure learning via conditional independence testing.
Introduces a Morse complex on symplectic manifolds using gradient flows and proves its cohomology is independent of metrics and Morse functions.
To each unit complex number with positive imaginary part there is defined a Tristram-Levine knot signature function. The set of all such signature functions is linearly independent as a set of functions defined on the set of all knots. The set of averaged signature functions forms a linearly independent set of homomoro…
We define a new smooth concordance homomorphism based on the knot Floer complex and an associated concordance invariant, epsilon. As an application, we show that an infinite family of topologically slice knots are independent in the smooth concordance group.
Paper extends learning theory to dependent data with uniform risk bounds.
Learning the Markov network structure from data is a problem that has received considerable attention in machine learning, and in many other application fields. This work focuses on a particular approach for this purpose called independence-based learning. Such approach guarantees the learning of the correct structure …
Novel tests for genetic independence in high-dimensional data.
Method discovers local independence in systems with continuous variables.
In this article we lay out the details of Fukaya's -structure of the Morse complexe of a manifold possibly with boundary. We show that this -structure is homotopically independent of the made choices. We emphasize the transversality arguments that make some fiber products smooth.
We present a new method for the separation of superimposed, independent, auto-correlated components from noisy multi-channel measurement. The presented method simultaneously reconstructs and separates the components, taking all channels into account and thereby increases the effective signal-to-noise ratio considerably…
This research designs a data-driven partition to test independence between continuous variables.
Study null conformal Killing vector fields on complex surfaces.
Proposes IPT for modeling complex joint distributions.
To reduce the label complexity in Agnostic Active Learning (A^2 algorithm), volume-splitting splits the hypothesis edges to reduce the Vapnik-Chervonenkis (VC) dimension in version space. However, the effectiveness of volume-splitting critically depends on the initial hypothesis and this problem is also known as target…
To improve the ability of VAE to disentangle in the latent space, existing works mostly focus on enforcing independence among the learned latent factors. However, the ability of these models to disentangle often decreases as the complexity of the generative factors increases. In this paper, we investigate the little-ex…
The paper offers generalization bounds for Transformers that ignore sequence length.
We obtain a tight distribution-specific characterization of the sample complexity of large-margin classification with L2 regularization: We introduce the margin-adapted dimension, which is a simple function of the second order statistics of the data distribution, and show distribution-specific upper and lower bounds on…
The paper tackles extrapolation in generative models by enforcing independence of mechanisms.
We address the problem of disentangled representation learning with independent latent factors in graph convolutional networks (GCNs). The current methods usually learn node representation by describing its neighborhood as a perceptual whole in a holistic manner while ignoring the entanglement of the latent factors. Ho…
In this paper, we introduce the concept of the independence graph of a directed 2-complex. We show that the class of diagram groups is closed under graph products over independence graphs of rooted 2-trees. This allows us to show that a diagram group containing all countable diagram groups is a semi-direct product of a…