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.
We solve the mean parametrization of von Mises-Fisher distribution.
We present a derivation of the Kullback Leibler (KL)-Divergence (also known as Relative Entropy) for the von Mises Fisher (VMF) Distribution in -dimensions.
Sparse prototypes improve clustering of high-dimensional directional data.
Mixture modelling involves explaining some observed evidence using a combination of probability distributions. The crux of the problem is the inference of an optimal number of mixture components and their corresponding parameters. This paper discusses unsupervised learning of mixture models using the Bayesian Minimum M…
A new method estimates the number of clusters on spherical data.
A new probabilistic approach improves deep metric learning by considering image uncertainties and class-specific variances.
New autoencoder improves latent space learning by optimizing sliced Gromov-Wasserstein discrepancies.
A drone-based MOT algorithm tracks vehicles using neural network detections and TPMBM filter.
A new distance metric for vMF distributions simplifies spherical data analysis.
Although stochastic gradient descent (SGD) is a driving force behind the recent success of deep learning, our understanding of its dynamics in a high-dimensional parameter space is limited. In recent years, some researchers have used the stochasticity of minibatch gradients, or the signal-to-noise ratio, to better char…
Proposes vMF distribution for skewed elliptical distributions.
The paper improves interpolation in generative models by using specific base distributions.
A new method for speaker recognition on hyperspheres improves on PLDA's limitations.
Generative models on spheres improve discrete sequence sampling.
Metric-based few-shot learning methods try to overcome the difficulty due to the lack of training examples by learning embedding to make comparison easy. We propose a novel algorithm to generate class representatives for few-shot classification tasks. As a probabilistic model for learned features of inputs, we consider…
The Variational Auto-Encoder (VAE) is one of the most used unsupervised machine learning models. But although the default choice of a Gaussian distribution for both the prior and posterior represents a mathematically convenient distribution often leading to competitive results, we show that this parameterization fails …
Learning suitable latent representations for observed, high-dimensional data is an important research topic underlying many recent advances in machine learning. While traditionally the Gaussian normal distribution has been the go-to latent parameterization, recently a variety of works have successfully proposed the use…
Study of filtering and smoothing in submanifolds of Euclidean space.
We propose a novel model for generating graphs similar to a given example graph. Unlike standard approaches that compute features of graphs in Euclidean space, our approach obtains features on a surface of a hypersphere. We then utilize a von Mises-Fisher distribution, an exponential family distribution on the surface …
Traditional topic models do not account for semantic regularities in language. Recent distributional representations of words exhibit semantic consistency over directional metrics such as cosine similarity. However, neither categorical nor Gaussian observational distributions used in existing topic models are appropria…
Score matching method improves density estimation for truncated data on manifolds.
T-PSDA improves speaker recognition accuracy on toroidal submanifolds.
We treat the problem of estimation of orientation parameters whose values are invariant to transformations from a spherical symmetry group. Previous work has shown that any such group-invariant distribution must satisfy a restricted finite mixture representation, which allows the orientation parameter to be estimated u…
This paper considers statistical estimation problems where the probability distribution of the observed random variable is invariant with respect to actions of a finite topological group. It is shown that any such distribution must satisfy a restricted finite mixture representation. When specialized to the case of dist…
A new probabilistic BTD method for tensor data.
The PARAFAC2 is a multimodal factor analysis model suitable for analyzing multi-way data when one of the modes has incomparable observation units, for example because of differences in signal sampling or batch sizes. A fully probabilistic treatment of the PARAFAC2 is desirable in order to improve robustness to noise an…
The modelling of data on a spherical surface requires the consideration of directional probability distributions. To model asymmetrically distributed data on a three-dimensional sphere, Kent distributions are often used. The moment estimates of the parameters are typically used in modelling tasks involving Kent distrib…
New summary measures reveal geometric structure in weighted measures on manifolds.
The Softmax function is used in the final layer of nearly all existing sequence-to-sequence models for language generation. However, it is usually the slowest layer to compute which limits the vocabulary size to a subset of most frequent types; and it has a large memory footprint. We propose a general technique for rep…
Proposes a new latent variable model for hyperspherical latent spaces.
Bayesian neural networks improve uncertainty calibration without sacrificing accuracy.
New normalizing flows for sphere distributions improve complexity and scale handling.
We consider the problem of subspace estimation in a Bayesian setting. Since we are operating in the Grassmann manifold, the usual approach which consists of minimizing the mean square error (MSE) between the true subspace and its estimate may not be adequate as the MSE is not the natural metric in the Gra…
A new distribution addresses scalability and numerical stability issues of the vMF.
Paper develops a new state estimation method for nonlinear systems.
Improves point-cloud reconstruction by optimizing projections with self-attention.
Symmetry helps VI recover certain statistics.
Generative models improve angular variable simulation in high dimensions.
We study rays in von Mangoldt planes, which has applications to the structure of open complete manifolds with lower radial curvature bounds. We prove that the set of souls of any rotationally symmetric plane of nonnegative curvature is a closed ball, and if the plane is von Mangoldt, we compute the radius of the ball. …
SAGE improves memory efficiency by selectively adding, merging, or ignoring new facts.
Study relative commutants in von Neumann algebras using contraction notions.
New Riemannian radial distributions help estimate parameters on symmetric spaces.
It is shown that the Novikov inequalities for critical points of closed 1-forms hold with the von Neumann Betti numbers replacing the Novikov numbers. As a corollary we obtain a vanishing theorem for cohomology, generalizing a theorem of W. Lueck. We also prove that von Neumann Betti numbers coincide with the Nov…
Paper generalizes kernel mean embedding to von Neumann-algebra-valued measures.
Develops diffusion models for time-varying correlation on the circle.
We study differential operators on complete Riemannian manifolds which act on sections of a bundle of finite type modules over a von Neumann algebra with a trace. We prove a relative index and a Callias-type index theorems for von Neumann indexes of such operators. We apply these results to obtain a version of Atiyah's…
Making use of its smooth structure only, out of a connected oriented smooth -manifold a von Neumann algebra is constructed. It is geometric in the sense that is generated by local operators and as a special four dimensional phenomenon it contains all algebraic (i.e., formal or coming from a metric) curvature tensors…
We prove a generalized version of the Strong Atiyah Conjecture for the infinite dihedral group W, replacing the group von Neumann algebra NW with the Hecke-von Neumann algebra N_qW.