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.
The paper introduces a frequency-domain estimator for low-order systems from noisy data.
The paper tackles system identification via Hankel nuclear norm regularization, improving estimation rates and singular value gaps.
New nonconvex methods improve SysID efficiency and accuracy.
Algorithm learns causal structures from low-order conditional independencies.
Develops method to construct Lie algebra weight system kernel using Vogel algebra.
We consider the problem of computing first-passage time distributions for reaction processes modelled by master equations. We show that this generally intractable class of problems is equivalent to a sequential Bayesian inference problem for an auxiliary observation process. The solution can be approximated efficiently…
GAMI-Tree uses model-based trees to fit low-order fANOVA models.
Climate projections continue to be marred by large uncertainties, which originate in processes that need to be parameterized, such as clouds, convection, and ecosystems. But rapid progress is now within reach. New computational tools and methods from data assimilation and machine learning make it possible to integrate …
Principal components analysis (PCA) is the optimal linear auto-encoder of data, and it is often used to construct features. Enforcing sparsity on the principal components can promote better generalization, while improving the interpretability of the features. We study the problem of constructing optimal sparse linear a…
With higher-order neighborhood information of graph network, the accuracy of graph representation learning classification can be significantly improved. However, the current higher order graph convolutional network has a large number of parameters and high computational complexity. Therefore, we propose a Hybrid Lower …
A new method interprets astrophysical spectra using geometric paths to distinguish line profiles.
Using the classification of transitive groups we classify indecomposable quandles of size <36. This classification is available in Rig, a GAP package for computations related to racks and quandles. As an application, the list of all indecomposable quandles of size <36 not of type D is computed.
The electroencephalography (EEG) source imaging problem is very sensitive to the electrical modelling of the skull of the patient under examination. Unfortunately, the currently available EEG devices and their embedded software do not take this into account; instead, it is common to use a literature-based skull conduct…
The moments of spatial probabilistic systems are often given by an infinite hierarchy of coupled differential equations. Moment closure methods are used to approximate a subset of low order moments by terminating the hierarchy at some order and replacing higher order terms with functions of lower order ones. For a give…
We introduce and study new invariants associated with Laplace type elliptic partial differential operators on manifolds. These invariants are constructed by using the off-diagonal heat kernel; they are not pure spectral invariants, that is, they depend not only on the eigenvalues but also on the corresponding eigenfunc…
Continuous-time Bayesian networks (CTBNs) constitute a general and powerful framework for modeling continuous-time stochastic processes on networks. This makes them particularly attractive for learning the directed structures among interacting entities. However, if the available data is incomplete, one needs to simulat…
We develop a systematic method for classifying supersymmetric orbifold compactifications of M-theory. By restricting our attention to abelian orbifolds with low order, in the special cases where elements do not include coordinate shifts, we construct a "periodic table" of such compactifications, organized according to …
Study local equivalence of Riemannian submersions using differential invariants.
Hermite polynomials improve private data generation by reducing feature count.
Efficient algorithm for matching graphs with community structure.
New framework detects out-of-distribution samples efficiently.
We introduce a notion of ternary distributive algebraic structure, give examples, and relate it to the notion of a quandle. Classification is given for low order structures of this type. Constructions of such structures from ternary bialgebras are provided. We also describe ternary distributive algebraic structures com…
The problem of low-rank approximation with convex constraints, which appears in data analysis, system identification, model order reduction, low-order controller design and low-complexity modelling is considered. Given a matrix, the objective is to find a low-rank approximation that meets rank and convex constraints, w…
New framework uses score-based priors to solve ill-conditioned polynomial equations, improving signal recovery from noisy data.
We define and study Vassiliev invariants for (long) Morse knots. It is shown that there are Vassiliev invariants which can distinguish some topologically equivalent Morse knots. In particular, there is an invariant of order 3 for Morse knots with one maximum that distinguishes two different representations of the figur…
This work provides a computationally efficient and statistically consistent moment-based estimator for mixtures of spherical Gaussians. Under the condition that component means are in general position, a simple spectral decomposition technique yields consistent parameter estimates from low-order observable moments, wit…
The concept of a C-class of differential equations goes back to E. Cartan with the upshot that generic equations in a C-class can be solved without integration. While Cartan's definition was in terms of differential invariants being first integrals, all results exhibiting C-classes that we are aware of are based on the…
We classify invariant Lagrangians of the form depending at most quadratically on the variables and , where is a Lorentz metric and is a tensor field of arbitrary rank on a smooth manifold. As a corollary, we prove a conjecture of Bray'…
This method infers models from data with physical insights, minimizing model order.
The objective of this paper is to investigate how noisy and incomplete observations can be integrated in the process of building a reduced-order model. This problematic arises in many scientific domains where there exists a need for accurate low-order descriptions of highly-complex phenomena, which can not be directly …
New fast estimation methods stemming from control theory lead to a fresh look at time series, which bears some resemblance to "technical analysis". The results are applied to a typical object of financial engineering, namely the forecast of foreign exchange rates, via a "model-free" setting, i.e., via repeated identifi…
Feature selection can facilitate the learning of mixtures of discrete random variables as they arise, e.g. in crowdsourcing tasks. Intuitively, not all workers are equally reliable but, if the less reliable ones could be eliminated, then learning should be more robust. By analogy with Gaussian mixture models, we seek a…
One of the most popular approaches to understanding feature effects of modern black box machine learning models are partial dependence plots (PDP). These plots are easy to understand but only able to visualize low order dependencies. The paper is about the question 'How much can we see?': A framework is developed to qu…
Notes on Whitney towers in 4-manifolds, focusing on local surface manipulations and invariants.
In the past decade, deep neural networks (DNNs) came to the fore as the leading machine learning algorithms for a variety of tasks. Their raise was founded on market needs and engineering craftsmanship, the latter based more on trial and error than on theory. While still far behind the application forefront, the theore…
Corrected moment-based methods improve inference in topic model regression.
Symbolic regression finds two projective invariants capturing most of the Ricci-flat metric variation.
Study shows transductive learning is equivalent to PAC learning for most natural loss functions.
Multi-agent coordination is prevalent in many real-world applications. However, such coordination is challenging due to its combinatorial nature. An important observation in this regard is that agents in the real world often only directly affect a limited set of neighbouring agents. Leveraging such loose couplings amon…
Presented are two neural network architectures for convex functions, demonstrating competitive performance.
This work studies applications and generalizations of a simple estimation technique that provides exponential concentration under heavy-tailed distributions, assuming only bounded low-order moments. We show that the technique can be used for approximate minimization of smooth and strongly convex losses, and specificall…
We consider the problem of learning mixtures of generalized linear models (GLM) which arise in classification and regression problems. Typical learning approaches such as expectation maximization (EM) or variational Bayes can get stuck in spurious local optima. In contrast, we present a tensor decomposition method whic…
Graph embedding has become a key component of many data mining and analysis systems. Current graph embedding approaches either sample a large number of node pairs from a graph to learn node embeddings via stochastic optimization or factorize a high-order proximity/adjacency matrix of the graph via computationally expen…
The reconstruction from observations of high-dimensional chaotic dynamics such as geophysical flows is hampered by (i) the partial and noisy observations that can realistically be obtained, (ii) the need to learn from long time series of data, and (iii) the unstable nature of the dynamics. To achieve such inference fro…
Investigates webs related to cluster algebras and polylogarithms.
Graph neural networks are currently leading the performance charts in learning-based molecule property prediction and classification. Computational chemistry has, therefore, become the a prominent testbed for generic graph neural networks, as well as for specialized message passing methods. In this work, we demonstrate…
A new method for non-rigid point set registration reduces computational complexity.
New method distinguishes predictive distribution estimators in high-dimensional inputs.