We propose a new type of generative model for high-dimensional data that learns a manifold geometry of the data, rather than density, and can generate points evenly along this manifold. This is in contrast to existing...
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Recent advances in single-cell RNA sequencing technologies enable deep insights into cellular development, gene regulation, and phenotypic diversity by measuring gene expression for thousands of cells in a single expe...
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We investigate the problem of automatically constructing efficient representations or basis functions for approximating value functions based on analyzing the structure and topology of the state space. In particular, ...
We investigate the problem of automatically constructing efficient representations or basis functions for approximating value functions based on analyzing the structure and topology of the state space. In particular, two novel approaches to value function approximation are explored based on automatically constructing basis functions on state spaces that can be represented as graphs or manifolds: one approach uses the eigenfunctions of the Laplacian, in effect performing a global Fourier analysis on the graph; the second approach is based on diffusion wavelets, which generalize classical wavelets to graphs using multiscale dilations induced by powers of a diffusion operator or random walk on the graph. Together, these approaches form the foundation of a new generation of methods for solving large Markov decision processes, in which the underlying representation and policies are simultaneously learned.
Though analyzing a single scalar field using Morse complexes is well studied, there are few techniques for visualizing a collection of Morse complexes. We focus on analyses that are enabled by looking at a Morse compl...
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Accurate and flexible representations of music data are paramount to addressing MIR tasks, yet many of the existing approaches are difficult to interpret or rigid in nature. This work introduces two new song represent...
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IT is the purpose of this letter first to point out that several independent lines of evidence seem to indicate that the ‘intercloud medium’ does not exist in its usually quoted state with density≳0.1 cm−3and temper...
IT is the purpose of this letter first to point out that several independent lines of evidence seem to indicate that the ‘intercloud medium’ does not exist in its usually quoted state with density≳0.1 cm−3and temperatureT∼104K. Rather, a hot, tenuous medium (n≲10−2cm−3,T∼106K) seems more consistent with observations in the neighbourhood of the Sun. That such might be the situation has been previously suggested (see refs 1 and 2). A mechanism for producing such a medium has been proposed by Cox and Smith3. Second, this letter points out several implications of such a “missing intercloud medium” on the large-scale structure of spiral galaxies.
At present, the most common and low-cost method to control the drone is to use a mobile phone with an APP. The operator takes his mobile phone screen as a human-machine interface, and at the same time controls and rec...
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Several classification methods assume that the underlying distributions follow tree-structured graphical models. Indeed, trees capture statistical dependencies between pairs of variables, which may be crucial to attai...
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Several classification methods assume that the underlying distributions follow tree-structured graphical models. Indeed, trees capture statistical dependencies between pairs of variables, which may be crucial to attaining low classification errors. In this setting, the optimal classifier is linear in the log-transformed univariate and bivariate densities that correspond to the tree edges. In practice, observed data may not be well approximated by trees. Yet, motivated by the importance of pairwise dependencies for accurate classification, here we propose to approximate the optimal decision boundary by a sparse linear combination of the univariate and bivariate log-transformed densities. Our proposed approach is semi-parametric in nature: we non-parametrically estimate the univariate and bivariate densities, remove pairs of variables that are nearly independent using the Hilbert-Schmidt independence criterion, and finally construct a linear SVM using the retained log-transformed densities. We demonstrate on synthetic and real data sets, that our classifier, named SLB (sparse log-bivariate density), is competitive with other popular classification methods.
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