arXiv research

Proposes random Euler filters for efficient complex-valued nonlinear signal processing.

We determine the expected curvature polynomial of random real projective varieties given as the zero set of independent random polynomials with Gaussian distribution, whose distribution is invariant under the action of the orthogonal group. In particular, the expected Euler characteristic of such random real projective…

Deep density methods improve filtering in high-dimensional systems.

The first purpose of this note is to comment on a recent article of Bursztyn, Lima and Meinrenken, in which it is proved that if M is a smooth submanifold of a manifold V, then there is a bijection between germs of tubular neighborhoods of M and germs of "Euler-like" vector fields on V. We shall explain how to approach…

Geometric approach solves Euler equations with random forces.

Research compares ML and Time Series methods for generating trading signals.

A new method for approximate inference using Wasserstein gradient flows.

The paper uses MRFs to improve recommendation accuracy in collaborative filtering.

To every tree we associate a filtered cochain complex. Its cohomology and the corresponding spectral sequence have clear combinatorial description. If a tree is the Dynkin diagram of a simple plane curve singularity, the graded Euler characteristic of this complex coincides with the Alexander polynomial of the link. In…

The bane of one-class collaborative filtering is interpreting and modelling the latent signal from the missing class. In this paper we present a novel Bayesian generative model for implicit collaborative filtering. It forms a core component of the Xbox Live architecture, and unlike previous approaches, delineates the o…

No-trick kernel adaptive filtering uses deterministic features for scalability and robustness.

This paper improves machine learning models' robustness against evasion attacks using randomness.

This study shows that certain cohomology groups of symplectic manifolds are always even-dimensional.

Defines a filtration on variational bicomplex for concise functional form conditions.

A new asymmetric correntropy method improves robust adaptive filtering for asymmetric error distributions.

This paper is concerned with nonlinear filtering of the coefficients in asset price models with stochastic volatility. More specifically, we assume that the asset price process $S=(S_{t})_{t\geq0}$ is given by \[ dS_{t}=m(θ_{t})S_{t} dt+v(θ_{t})S_{t} dB_{t}, \] where $B=(B_{t})_{t\geq0}$ is a Brownian motion, $v$ is a …

This paper is concerned with nonlinear filtering of the coefficients in asset price models with stochastic volatility. More specifically, we assume that the asset price process $S=(S_{t})_{t\geq0}$ is given by \[ dS_{t}=r(θ_{t})S_{t}dt+v(θ_{t})S_{t}dB_{t}, \] where $B=(B_{t})_{t\geq0}$ is a Brownian motion, $v$ is a …

We examine the relationship between the (untwisted) knot Floer cube of resolutions and HOMFLY-PT homology. By using a filtration induced by additional basepoints on the Heegaard diagram for a knot $K$, we see that the filtered complex decomposes as a direct sum of HOMFLY-PT homologies of various subdiagrams. Jaeger's c…

Motivated by problems in search and detection we present a solution to a Combinatorial Multi-Armed Bandit (CMAB) problem with both heavy-tailed reward distributions and a new class of feedback, filtered semibandit feedback. In a CMAB problem an agent pulls a combination of arms from a set $\{1,...,k\}$ in each round, g…

We introduce a covariance matrix estimator that both takes into account the heteroskedasticity of financial returns (by using an exponentially weighted moving average) and reduces the effective dimensionality of the estimation (and hence measurement noise) via techniques borrowed from random matrix theory. We calculate…

A new feature selection method using random forest and Kolmogorov filter.

Paper solves complex signal processing problem efficiently.

Improved Kalman filter for non-linear, non-Gaussian data.

New explanation of reservoir computing using random projections.

Efficiently computes sparse signature coefficients using kernels.

Dropout neural networks can approximate any function with high probability.

Study examines how COVID-19 affects bond yields using network filtering methods.

Following the approach of standard filtering theory, we analyse investor-valuation of firms, when these are modelled as geometric-Brownian state processes that are privately and partially observed, at random (Poisson) times, by agents. Tasked with disclosing forecast values, agents are able purposefully to withhold the…

The problem of filtering information from large correlation matrices is of great importance in many applications. We have recently proposed the use of the Kullback-Leibler distance to measure the performance of filtering algorithms in recovering the underlying correlation matrix when the variables are described by a mu…

Gradient descent in Gaussian random fields helps understand high-dimensional optimization problems.

We prove that the Euler form of a metric connection on real oriented vector bundle $E$ over a compact oriented manifold $M$ can be identified, as a current, with the expectation of the random current defined by the zero-locus of a certain random section of the bundle. We also explain how to reconstruct probabilisticall…

The paper introduces a quantum state system to count perfect matchings in graphs.

In this paper we examine the effect of applying ensemble learning to the performance of collaborative filtering methods. We present several systematic approaches for generating an ensemble of collaborative filtering models based on a single collaborative filtering algorithm (single-model or homogeneous ensemble). We pr…

DCFNet decomposes CNN filters into learned coefficients with bases, reducing parameters and computation.

We write the Euler characteristic X(G) of a four dimensional finite simple geometric graph G=(V,E) in terms of the Euler characteristic X(G(w)) of two-dimensional geometric subgraphs G(w). The Euler curvature K(x) of a four dimensional graph satisfying the Gauss-Bonnet relation sum_x K(x) = X(G) can so be rewritten as …

Introduces numerical Gaussian process Kalman filtering for infinite-dimensional systems.

We study empirical covariance matrices in finance. Due to the limited amount of available input information, these objects incorporate a huge amount of noise, so their naive use in optimization procedures, such as portfolio selection, may be misleading. In this paper we investigate a recently introduced filtering proce…

Develops a method for random manifolds and submanifolds, focusing on 3-ball knots.

New methods learn sampling distributions for particle filters without supervision.

Simplified analysis of diffusion models using discrete random variables.

We consider a finite simplicial complex $K$ together with its successive barycentric subdivisions $Sd^d(K), d\geq0,$ and study the expected topology of a random subcomplex in $Sd^d(K), d\gg0$. We get asymptotic upper and lower bounds for the expected Betti numbers of those subcomplexes, together with the average Morse …

Rating prediction is an important application, and a popular research topic in collaborative filtering. However, both the validity of learning algorithms, and the validity of standard testing procedures rest on the assumption that missing ratings are missing at random (MAR). In this paper we present the results of a us…

Enhanced SMC$^2$ uses gradients from CRN-PF in Langevin proposals for improved state and parameter estimation.

Recommender systems play a central role in providing individualized access to information and services. This paper focuses on collaborative filtering, an approach that exploits the shared structure among mind-liked users and similar items. In particular, we focus on a formal probabilistic framework known as Markov rand…

AOFP prunes CNN filters faster and more accurately.

New method for identifying graph shift operators using vertex-time autoregressive models.

There is much empirical evidence that item-item collaborative filtering works well in practice. Motivated to understand this, we provide a framework to design and analyze various recommendation algorithms. The setup amounts to online binary matrix completion, where at each time a random user requests a recommendation a…

The paper analyzes how gradient descent learns convolutional filters for non-Gaussian inputs.