相关论文: Densities, spectral densities and modality

We consider the problem of estimating the population probability distribution given a finite set of multivariate samples, using the maximum entropy approach. In strict keeping with Jaynes' original definition, our precise formulation of the…

Density estimation is a versatile technique underlying many data mining tasks and techniques,ranging from exploration and presentation of static data, to probabilistic classification, or identifying changes or irregularities in streaming…

Regular sequences are natural generalisations of fixed points of constant-length substitutions on finite alphabets, that is, of automatic sequences. Using the harmonic analysis of measures associated with substitutions as motivation, we…

The crucial step in designing a particle filter for a particular application is the choice of importance density. The optimal scheme is to use the conditional posterior density of the state, but this cannot be sampled or calculated…

The spectral density matrix is a fundamental object of interest in time series analysis, and it encodes both contemporary and dynamic linear relationships between component processes of the multivariate system. In this paper we develop…

This study aims to publish a novel similarity metric to increase the speed of comparison operations. Also the new metric is suitable for distance-based operations among strings. Most of the simple calculation methods, such as string length…

Spectral clustering is a powerful method for finding structure in a dataset through the eigenvectors of a similarity matrix. It often outperforms traditional clustering algorithms such as $k$-means when the structure of the individual…

Density-based clustering relies on the idea of linking groups to some specific features of the probability distribution underlying the data. The reference to a true, yet unknown, population structure allows to frame the clustering problem…

In this paper we propose methods for inference of the geometric features of a multivariate density. Our approach uses multiscale tests for the monotonicity of the density at arbitrary points in arbitrary directions. In particular, a…

Machine learning models suffer from overfitting, which is caused by a lack of labeled data. To tackle this problem, we proposed a framework of regularization methods, called density-fixing, that can be used commonly for supervised and…

We exhibit an explicit formula for the spectral density of a (large) random matrix which is a diagonal matrix whose spectral density converges, perturbated by the addition of a symmetric matrix with Gaussian entries and a given (small)…

We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…

Estimating the density of a continuous random variable X has been studied extensively in statistics, in the setting where n independent observations of X are given a priori and one wishes to estimate the density from that. Popular methods…

Approximate model counting for bit-vector SMT formulas (generalizing \#SAT) has many applications such as probabilistic inference and quantitative information-flow security, but it is computationally difficult. Adding random parity…

Expand-and-sparsify representations are a class of theoretical models that capture sparse representation phenomena observed in the sensory systems of many animals. At a high level, these representations map an input $x \in \mathbb{R}^d$ to…

In hep-th/0111281 the complete set of eigenvectors and eigenvalues of Neumann matrices was found. It was shown also that the spectral density contains a divergent constant piece that being regulated by truncation at level L equals (log…

We develop methodology allowing to simulate a stationary functional time series defined by means of its spectral density operators. Our framework is general, in that it encompasses any such stationary functional time series, whether linear…

The paper investigates dynamical systems for which the derivative of some positive-definite function along the solutions of this system depends on so-called density function. In turn, such dynamical systems are called density systems. The…

The spectral representation separates the contributions of geometrical arrangement (topology) and intrinsic constituent properties in a composite. The aim of paper is to present a numerical algorithm based on the Monte Carlo integration and…

Density functional theory has become the world's favorite electronic structure method, and is routinely applied to both materials and molecules. Here, we review recent attempts to use modern machine-learning to improve density functional…