arXiv research

Note: Causality can be encoded without strict time function choice.

Auto-encoders are among the most popular neural network architecture for dimension reduction. They are composed of two parts: the encoder which maps the model distribution to a latent manifold and the decoder which maps the latent manifold to a reconstructed distribution. However, auto-encoders are known to provoke cha…

A new model encodes distances and topology in latent variables.

Extends graph encoder embedding to weighted graphs and matrices.

MUTE improves neural network performance with efficient target encoding.

Null distance encodes causal structure in spacetimes.

We propose the Wasserstein Auto-Encoder (WAE)---a new algorithm for building a generative model of the data distribution. WAE minimizes a penalized form of the Wasserstein distance between the model distribution and the target distribution, which leads to a different regularizer than the one used by the Variational Aut…

Proves globally hyperbolic spacetimes via null distance completeness.

Study extends null distance concept to Lorentzian length spaces for spacetime analysis.

This paper proposes grid cells encode position via a conformal isometric embedding of 2D physical space.

The Wasserstein distance and its variations, e.g., the sliced-Wasserstein (SW) distance, have recently drawn attention from the machine learning community. The SW distance, specifically, was shown to have similar properties to the Wasserstein distance, while being much simpler to compute, and is therefore used in vario…

Generative models use DAE or DSM to estimate score, then Langevin sampling for sampling.

In the economic literature, geographic distances are considered fundamental factors to be included in any theoretical model whose aim is the quantification of the trade between countries. Quantitatively, distances enter into the so-called gravity models that successfully predict the weight of non-zero trade flows. Howe…

DE improves GNNs by distinguishing graph substructures, enhancing accuracy.

DAG-WGAN learns causal structures using Wasserstein distance.

We present a novel hierarchical distance-dependent Bayesian model for event coreference resolution. While existing generative models for event coreference resolution are completely unsupervised, our model allows for the incorporation of pairwise distances between event mentions -- information that is widely used in sup…

Improved reliability of machine learning predictions using variational auto-encoders.

Optimal transport offers an alternative to maximum likelihood for learning generative autoencoding models. We show that minimizing the p-Wasserstein distance between the generator and the true data distribution is equivalent to the unconstrained min-min optimization of the p-Wasserstein distance between the encoder agg…

Distance between evolving hypersurfaces is a PDE solution.

Develops a new non-adversarial framework for better generative models.

We propose a non-parametric regression methodology, Random Forests on Distance Matrices (RFDM), for detecting genetic variants associated to quantitative phenotypes representing the human brain's structure or function, and obtained using neuroimaging techniques. RFDM, which is an extension of decision forests, requires…

Acoustic Neighbor Embeddings map speech and text to fixed dimensions for phonetic confusability.

BinConv improves time series forecasting by preserving ordinal information in a classification framework.

In this paper, we present a simple non-parametric method for learning the structure of undirected graphs from data that drawn from an underlying unknown distribution. We propose to use Brownian distance covariance to estimate the conditional independences between the random variables and encodes pairwise Markov graph. …

The paper explores a new type of kernel using Wasserstein distance for better classification of shapes.

Generative adversarial nets (GANs) and variational auto-encoders have significantly improved our distribution modeling capabilities, showing promise for dataset augmentation, image-to-image translation and feature learning. However, to model high-dimensional distributions, sequential training and stacked architectures …

It is a generally shared opinion that significant information about the topology of a bounded domain $Ω$ of a riemannian manifold $M$ is encoded into the properties of the distance, $d_{\partialΩ}$, %, $d:Ω\rightarrow [0,\infty [$, from the boundary of $Ω$. To confirm such an idea we propose an approach based on the in…

The paper shows how to recover true node positions from a graph or similarity matrix.

Paper estimates non-causal graphical models using covariance extension and transportation distance.

Optimal transport theory has recently found many applications in machine learning thanks to its capacity for comparing various machine learning objects considered as distributions. The Kantorovitch formulation, leading to the Wasserstein distance, focuses on the features of the elements of the objects but treat them in…

Permutation invariant network learns Wasserstein metrics.

We study unsupervised generative modeling in terms of the optimal transport (OT) problem between true (but unknown) data distribution $P_X$ and the latent variable model distribution $P_G$. We show that the OT problem can be equivalently written in terms of probabilistic encoders, which are constrained to match the pos…

We present a methodology for clustering N objects which are described by multivariate time series, i.e. several sequences of real-valued random variables. This clustering methodology leverages copulas which are distributions encoding the dependence structure between several random variables. To take fully into account …

Graphon autoencoder generates graphs with arbitrary sizes using Chebyshev filters.

Fisher auto-encoders use Fisher divergence for more robust generative modeling.

Study clusters bank customers using LSTM and DTW.

We report on experimental measurement of the Hilbert-Schmidt distance between two two-qubit states by many-particle interference. We demonstrate that our three-step method for measuring distances in Hilbert space is far less complex than reconstructing density matrices and that it can be applied in quantum-enhanced mac…

Vectors of data are at the heart of machine learning and data mining. Recently, vector quantization methods have shown great promise in reducing both the time and space costs of operating on vectors. We introduce a vector quantization algorithm that can compress vectors over 12x faster than existing techniques while al…

New measures assess differences in causal graphs' separations.

This study rethinks the latent space in generative modeling, improving performance with less complex models.

A new spherical Sliced-Wasserstein distance for data on spheres.

Hierarchical clustering is a class of algorithms that seeks to build a hierarchy of clusters. It has been the dominant approach to constructing embedded classification schemes since it outputs dendrograms, which capture the hierarchical relationship among members at all levels of granularity, simultaneously. Being gree…

Improves energy efficiency of neuromorphic hardware by optimizing memory organization and encoding schemes.

Improves latent space structure for better data representation.

We consider the problem of learning a measure of distance among vectors in a feature space and propose a hybrid method that simultaneously learns from similarity ratings assigned to pairs of vectors and class labels assigned to individual vectors. Our method is based on a generative model in which class labels can prov…

The paper proves uniform Temple charts and applies them to null distance metrics.

Most speech recognition tasks pertain to mapping words across two modalities: acoustic and orthographic. In this work, we suggest learning encoders that map variable-length, acoustic or phonetic, sequences that represent words into fixed-dimensional vectors in a shared latent space; such that the distance between two w…

We study minimax convergence rates of nonparametric density estimation under a large class of loss functions called "adversarial losses", which, besides classical $\mathcal{L}^p$ losses, includes maximum mean discrepancy (MMD), Wasserstein distance, and total variation distance. These losses are closely related to the …