相关论文: On the Size of the Online Kernel Sparsification Di…

Gaussian graphical models are widely used to represent correlations among entities but remain vulnerable to data corruption. In this work, we introduce a modified trimmed-inner-product algorithm to robustly estimate the covariance in an…

Convolutional sparse coding (CSC) has been popularly used for the learning of shift-invariant dictionaries in image and signal processing. However, existing methods have limited scalability. In this paper, instead of convolving with a…

How many words are needed to define all the words in a dictionary? Graph-theoretic analysis reveals that about 10% of a dictionary is a unique Kernel of words that define one another and all the rest, but this is not the smallest such…

We explore leveraging corpus-specific vocabularies that improve both efficiency and effectiveness of learned sparse retrieval systems. We find that pre-training the underlying BERT model on the target corpus, specifically targeting…

Algorithms involving Gaussian processes or determinantal point processes typically require computing the determinant of a kernel matrix. Frequently, the latter is computed from the Cholesky decomposition, an algorithm of cubic complexity in…

We consider a size-structured population describing the cell divisions. The cell population is described by an empirical measure and we observe the divisions in the continuous time interval [0, T ]. We address here the problem of estimating…

Dictionary learning is the problem of estimating the collection of atomic elements that provide a sparse representation of measured/collected signals or data. This paper finds fundamental limits on the sample complexity of estimating…

This paper proposes a novel kernel approach to linear dimension reduction for supervised learning. The purpose of the dimension reduction is to find directions in the input space to explain the output as effectively as possible. The…

Kernel density estimation is a widely used nonparametric approach to estimate an unknown distribution. Recent work in Bayesian predictive inference has considered stochastic processes formed by specifying the predictive distribution for the…

This paper studies the question of how well a signal can be reprsented by a sparse linear combination of reference signals from an overcomplete dictionary. When the dictionary size is exponential in the dimension of signal, then the exact…

Let $\mathfrak{O}$ be a compact discrete valuation ring of characteristic zero. Given a module $M$ of matrices over $\mathfrak{O}$, we study the generating function encoding the average sizes of the kernels of the elements of $M$ over…

We propose a sparse algebra for samplet compressed kernel matrices, to enable efficient scattered data analysis. We show the compression of kernel matrices by means of samplets produces optimally sparse matrices in a certain S-format. It…

The use of kernels for nonlinear prediction is widespread in machine learning. They have been popularized in support vector machines and used in kernel ridge regression, amongst others. Kernel methods share three aspects. First, instead of…

This paper develops a nonlinear operator dynamic that progressively removes the influence of a prescribed feature subspace while retaining maximal structure elsewhere. The induced sequence of positive operators is monotone, admits an exact…

This paper uses computational experiments to explore the role of exposure in the emergence of construction grammars. While usage-based grammars are hypothesized to depend on a learner's exposure to actual language use, the mechanisms of…

We present DepCC, the largest-to-date linguistically analyzed corpus in English including 365 million documents, composed of 252 billion tokens and 7.5 billion of named entity occurrences in 14.3 billion sentences from a web-scale crawl of…

This article treats the problem of learning a dictionary providing sparse representations for a given signal class, via $\ell_1$-minimisation. The problem can also be seen as factorising a $\ddim \times \nsig$ matrix $Y=(y_1 >... y_\nsig),…

Treebanks, such as the Penn Treebank (PTB), offer a simple approach to obtaining a broad coverage grammar: one can simply read the grammar off the parse trees in the treebank. While such a grammar is easy to obtain, a square-root rate of…

How many words (and which ones) are sufficient to define all other words? When dictionaries are analyzed as directed graphs with links from defining words to defined words, they reveal a latent structure. Recursively removing all words that…

To investigate a dilemma of statistical and computational efficiency faced by long-run variance estimators, we propose a decomposition of kernel weights in a quadratic form and some online inference principles. These proposals allow us to…