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.
Paper proposes bypassing implicit assumption in GM-based AD methods.
Two of the most popular modelling paradigms in computer vision are feed-forward neural networks (FFNs) and probabilistic graphical models (GMs). Various connections between the two have been studied in recent works, such as e.g. expressing mean-field based inference in a GM as an FFN. This paper establishes a new conne…
Unified framework for generative models incorporating VAE and GAN.
New GM layers improve neural network performance.
Bi-flat F-structures link to differential bicomplexes and Gauss-Manin connections.
This paper investigates whether the gravity model (GM) can explain the statistical properties of the International Trade Network (ITN). We fit data on international-trade flows with a GM specification using alternative fitting techniques and we employ GM estimates to build a weighted predicted ITN, whose topological pr…
Given a graphical model (GM), computing its partition function is the most essential inference task, but it is computationally intractable in general. To address the issue, iterative approximation algorithms exploring certain local structure/consistency of GM have been investigated as popular choices in practice. Howev…
We prove the universal lifting theorem: for an -simply connected and -connected Lie groupoid $\gm$ with Lie algebroid , the graded Lie algebra of multi-differentials on is isomorphic to that of multiplicative multi-vector fields on $\gm$. As a consequence, we obtain the integration theorem for a quasi-Lie …
Learning parameters of latent graphical models (GM) is inherently much harder than that of no-latent ones since the latent variables make the corresponding log-likelihood non-concave. Nevertheless, expectation-maximization schemes are popularly used in practice, but they are typically stuck in local optima. In the rece…
Solves Deligne-Simpson problem for special connections on Gm.
The paper tackles fairness in estimating graphical models, especially for protected attributes.
New formula and properties of inverted Habiro series derived from GM series.
Computing partition function is the most important statistical inference task arising in applications of Graphical Models (GM). Since it is computationally intractable, approximate methods have been used to resolve the issue in practice, where mean-field (MF) and belief propagation (BP) are arguably the most popular an…
A natural way of handling imbalanced data is to attempt to equalise the class frequencies and train the classifier of choice on balanced data. For two-class imbalanced problems, the classification success is typically measured by the geometric mean (GM) of the true positive and true negative rates. Here we prove that G…
Generative models (GMs) such as Generative Adversary Network (GAN) and Variational Auto-Encoder (VAE) have thrived these years and achieved high quality results in generating new samples. Especially in Computer Vision, GMs have been used in image inpainting, denoising and completion, which can be treated as the inferen…
This work examines consistency issues in Gaussian Mixture Model reduction algorithms.
Partial Label Learning (PLL) aims to learn from the data where each training example is associated with a set of candidate labels, among which only one is correct. The key to deal with such problem is to disambiguate the candidate label sets and obtain the correct assignments between instances and their candidate label…
Let be a smooth area decreasing map between two Riemannian manifolds $(M,\gm)$ and $(N,\gn)$. Under weak and natural assumptions on the curvatures of $(M,\gm)$ and $(N,\gn)$, we prove that the mean curvature flow provides a smooth homotopy of to a constant map.
Plug-and-play L-GM-AMP improves CS recovery for any i.i.d. source prior.
The Gibbs sampler is a particularly popular Markov chain used for learning and inference problems in Graphical Models (GMs). These tasks are computationally intractable in general, and the Gibbs sampler often suffers from slow mixing. In this paper, we study the Swendsen-Wang dynamics which is a more sophisticated Mark…
Paper shows how to use geometric median for robust SGD in high dimensions.
We propose a four-layer fully-connected neural network (FNN) for predicting fluid intelligence scores from T1-weighted MR images for the ABCD-challenge. In addition to the volumes of brain structures, the FNN uses cortical WM/GM contrast and cortical thickness at 78 cortical regions. These last two measurements were de…
New framework uses symmetry-based matrices for efficient, flexible NNs.
Optimizes portfolios with GM returns using convex optimization.
Proposes GM Score to evaluate GANs considering diversity, disentanglement, and discriminability.
This paper means to correct an error by the authors for the composite case in the paper "Lens Spaces, Isospectral on Forms but not on Functions", published in LMS J. Comput. Math.} 9 (2006), 270-286. All calculations and examples presented in \cite{GM} for prime remain valid, and we include detailed calculation…
Within crystallization theory, (Matveev's) complexity of a 3-manifold can be estimated by means of the combinatorial notion of GM-complexity. In this paper, we prove that the GM-complexity of any lens space L(p,q), with p greater than 2, is bounded by S(p,q)-3, where S(p,q) denotes the sum of all partial quotients in t…
This paper introduces a new probabilistic architecture called Sum-Product Graphical Model (SPGM). SPGMs combine traits from Sum-Product Networks (SPNs) and Graphical Models (GMs): Like SPNs, SPGMs always enable tractable inference using a class of models that incorporate context specific independence. Like GMs, SPGMs p…
In this paper we review a geometric approach to PDEs. We mainly focus on scalar PDEs in n independent variables and one dependent variable of order one and two, by insisting on the underlying (2n+1)-dimensional contact manifold and the so-called Lagrangian Grassmannian bundle over the latter. This work is based on a 30…
As a step toward proving an index theorem for hypoelliptic operators Heisenberg manifolds, including those on CR and contact manifolds, we construct an analogue for Heisenberg manifolds of Connes' tangent groupoid of a manifold . As it is well known for a Heisenberg manifold the relevant notion of tangent is…
Consider the moduli space of parabolic Higgs bundles (E,Φ) of rank two on CP^1 such that the underlying holomorphic vector bundle for the parabolic vector bundle E is trivial. It is equipped with the natural involution defined by (E,Φ)\mapsto (E,-Φ). We study the fixed point locus of this involution. In [GM], this modu…
Let F be a Riemannian submersion from an almost Hermitian manifold (M; gM; J) onto a Riemannian manifold (N; gN). We introduce the notion of the semi-slant submersion. And then we obtain some properties about it. In particular, we give some examples for it.
Let F be a Riemannian submersion from an almost Hermitian manifold (M; gM; J) onto a Riemannian manifold (N; gN). We introduce the notion of the v-semi-slant submersion. And then we obtain some properties on it. In particular, we give some examples for it.
We show the local rigidity of complex hyperbolic lattices in classical Hermitian semisimple Lie groups, . This reproves or generalizes some results in \cite{GM, KKP, Klingler-inv, Pozzetti}.
We studied isometric stochastic flows of a Stratonovich stochastic differential equation on spheres, i.e. on the standard sphere and Gromoll-Meyer exotic sphere. The standard sphere can be constructed as the quotient manifold with the so-called -action of , where…
Innovative series invariant for knot complements, linking to existing invariants.
Geometric models improve feature extraction and equivariance in image generation.
Markov Chain Monte Carlo (MCMC) and Belief Propagation (BP) are the most popular algorithms for computational inference in Graphical Models (GM). In principle, MCMC is an exact probabilistic method which, however, often suffers from exponentially slow mixing. In contrast, BP is a deterministic method, which is typicall…
Generative Adversarial Networks (GANs) have been shown to produce realistically looking synthetic images with remarkable success, yet their performance seems less impressive when the training set is highly diverse. In order to provide a better fit to the target data distribution when the dataset includes many different…
We propose a novel graphical model selection (GMS) scheme for high-dimensional stationary time series or discrete time process. The method is based on a natural generalization of the graphical LASSO (gLASSO), introduced originally for GMS based on i.i.d. samples, and estimates the conditional independence graph (CIG) o…
Paper learns Cartesian product graphs with Laplacian constraints.
We prove, under some mild conditions, that the equivariant twisted K-theory group of a crossed module admits a ring structure if the twisting 2-cocycle is 2-multiplicative. We also give an explicit construction of the transgression map for any crossed module and prove…
GMVAEs cluster and generate game levels without labels.
Classifier ensembles are pattern recognition structures composed of a set of classification algorithms (members), organized in a parallel way, and a combination method with the aim of increasing the classification accuracy of a classification system. In this study, we investigate the application of a generalized mixtur…
New method uses TT approximations to solve HJB equations for efficient sampling.
This paper presents a solution for persistent monitoring of real-world stochastic phenomena, where the underlying covariance structure changes sharply across time, using a small number of mobile robot sensors. We propose an adaptive solution for the problem where stochastic real-world dynamics are modeled as a Gaussian…
Characterizes GM-groups via sub-Riemannian geometry properties.
SLERP interpolation optimizes dynamic weight rebalancing in AMMs.