arXiv research

Obtaining complete information about the shape of an object by looking at it from a single direction is impossible in general. In this paper, we theoretically study obtaining differential geometric information of an object from orthogonal projections in a number of directions. We discuss relations between (1) a space c…

Approximate inference via information projection has been recently introduced as a general-purpose approach for efficient probabilistic inference given sparse variables. This manuscript goes beyond classical sparsity by proposing efficient algorithms for approximate inference via information projection that are applica…

We present a number of conditions which are necessary for an n-dimensional projective structure (M,[nabla]) to include the Levi-Civita connection nabla of some metric on M. We provide an algorithm, which effectively checks if a Levi-Civita connection is in the projective class and, in the positive, which finds this con…

We analyse the structure of local martingale deflators projected on smaller filtrations. In a general continuous-path setting, we show that the local martingale part in the multiplicative Doob-Meyer decomposition of projected local martingale deflators are themselves local martingale deflators in the smaller informatio…

The paper studies projections of asset prices under equivalent martingale measures.

A new indicator measures project risk from activity durations.

We give a criterion for a projective surface to become a quotient of a fake projective plane. We also give a detailed information on the elliptic fibration of a $(2,3)$-elliptic surface that is the minimal resolution of a quotient of a fake projective plane. As a consequence, we give a classification of ${\mathbb Q}$-h…

Proposes TS-NMF for 2D clustering, preserving spatial info.

The use of orthogonal projections on high-dimensional input and target data in learning frameworks is studied. First, we investigate the relations between two standard objectives in dimension reduction, preservation of variance and of pairwise relative distances. Investigations of their asymptotic correlation as well a…

Develops optimal low-dimensional approximations to high-dimensional SDEs.

We introduce a method, KL-LIME, for explaining predictions of Bayesian predictive models by projecting the information in the predictive distribution locally to a simpler, interpretable explanation model. The proposed approach combines the recent Local Interpretable Model-agnostic Explanations (LIME) method with ideas …

MILDA uses unlabelled data to compute LDA projections.

Information theoretical measures, such as entropy, mutual information, and various divergences, exhibit robust characteristics in image registration applications. However, the estimation of these quantities is computationally intensive in high dimensions. On the other hand, consistent estimation from pairwise distances…

Modelling highly multi-modal data is a challenging problem in machine learning. Most algorithms are based on maximizing the likelihood, which corresponds to the M(oment)-projection of the data distribution to the model distribution. The M-projection forces the model to average over modes it cannot represent. In contras…

Paper proposes PPMM for fast estimation of large-scale OTM.

We propose a generic, Bayesian, information geometric approach to the exploration--exploitation trade-off in multi-armed bandit problems. Our approach, BelMan, uniformly supports pure exploration, exploration--exploitation, and two-phase bandit problems. The knowledge on bandit arms and their reward distributions is su…

Implementing large-scale information and communication technology (IT) projects carries large risks and easily might disrupt operations, waste taxpayers' money, and create negative publicity. Because of the high risks it is important that government leaders manage the attendant risks. We analysed a sample of 1,355 publ…

Two-dimensional embeddings remain the dominant approach to visualize high dimensional data. The choice of embeddings ranges from highly non-linear ones, which can capture complex relationships but are difficult to interpret quantitatively, to axis-aligned projections, which are easy to interpret but are limited to biva…

Zero-shot learning transfers knowledge from seen classes to novel unseen classes to reduce human labor of labelling data for building new classifiers. Much effort on zero-shot learning however has focused on the standard multi-class setting, the more challenging multi-label zero-shot problem has received limited attent…

Sensor drift is a well-known issue in the field of sensors and measurement and has plagued the sensor community for many years. In this paper, we propose a sensor drift correction method to deal with the sensor drift problem. Specifically, we propose a discriminative subspace projection approach for sensor drift reduct…

Optimal persuasion involves projecting state vectors onto lower-dimensional 'optimal information manifolds'.

Develops accelerated methods for optimization using low-dimensional projected-gradient information.

The paper solves portfolio selection using Rényi divergence and optimization.

Flow cytometry is often used to characterize the malignant cells in leukemia and lymphoma patients, traced to the level of the individual cell. Typically, flow cytometric data analysis is performed through a series of 2-dimensional projections onto the axes of the data set. Through the years, clinicians have determined…

We study the problem of supervised linear dimensionality reduction, taking an information-theoretic viewpoint. The linear projection matrix is designed by maximizing the mutual information between the projected signal and the class label (based on a Shannon entropy measure). By harnessing a recent theoretical result on…

Determines higher smooth surgery structure sets of complex projective spaces.

InfoOT improves data alignment by maximizing mutual information.

The paper explores projective structures on curves and their applications in conformal geometry.

Sliced-Wasserstein distance (SW) and its variant, Max Sliced-Wasserstein distance (Max-SW), have been used widely in the recent years due to their fast computation and scalability even when the probability measures lie in a very high dimensional space. However, SW requires many unnecessary projection samples to approxi…

The curse of dimensionality is a longstanding challenge in Bayesian inference in high dimensions. In this work, we propose a projected Stein variational gradient descent (pSVGD) method to overcome this challenge by exploiting the fundamental property of intrinsic low dimensionality of the data informed subspace stemmin…

A new method optimizes projection directions for sliced Wasserstein distances.

New model estimates higher-order interactions in stochastic processes using lower-dimensional projections.

Physics-informed neural networks improve by measuring effective dimensionality of constraints.

We propose a projection pursuit (PP) algorithm based on Gaussian mixture models (GMMs). The negentropy obtained from a multivariate density estimated by GMMs is adopted as the PP index to be maximised. For a fixed dimension of the projection subspace, the GMM-based density estimation is projected onto that subspace, wh…

This paper tabulates prime knot projections up to eight double points.

A method to visualize multidimensional local subspaces using implicit differentiation.

Random projections help in representing sparse graphs efficiently.

By considering the projectivized spectrum of the Jacobi operator, we introduce the concept of projective Osserman manifold in both the affine and in the pseudo-Riemannian settings. If M is an affine projective Osserman manifold, then the modified Riemannian extension metric on the cotangent bundle is both spacelike and…

We consider an important class of signal processing problems where the signal of interest is known to be sparse, and can be recovered from data given auxiliary information about how the data was generated. For example, a sparse Green's function may be recovered from seismic experimental data using sparsity optimization…

STAR improves equivariant and invariant representation learning by routing projection heads.

A new ensemble method using random projections for kNN classification.

Geometric theory of projection heads in self-supervised learning.

Paper introduces a new project control method using Monte Carlo and statistical learning.

In this paper, we study a refined L2 version of the semiclassical approximation of projectively invariant elliptic operators with invariant Morse type potentials on covering spaces of compact manifolds. We work on the level of spectral projections (and not just their traces) and obtain an information about classes of t…

We construct Hodge filtered cohomology groups for complex manifolds that combine the topological information of generalized cohomology theories with geometric data of Hodge filtered holomorphic forms. This theory provides a natural generalization of Deligne cohomology. For smooth complex algebraic varieties, we show th…

We tackle the problem disentangling the latent space of an autoencoder in order to separate labelled attribute information from other characteristic information. This then allows us to change selected attributes while preserving other information. Our method, matrix subspace projection, is much simpler than previous ap…

Exploits class similarity for better machine learning models with confidence labels and projective loss functions.

Researchers study spectral asymmetry using pseudodifferential projections on the massless Dirac operator.