22,805 research outputs found
A Unifying review of linear gaussian models
Factor analysis, principal component analysis, mixtures of gaussian clusters, vector quantization, Kalman filter models, and hidden Markov models can all be unified as variations of unsupervised learning under a single basic generative model. This is achieved by collecting together disparate observations and derivations made by many previous authors and introducing a new way of linking discrete and continuous state models using a simple nonlinearity. Through the use of other nonlinearities, we show how independent component analysis is also a variation of the same basic generative model.We show that factor analysis and mixtures of gaussians can be implemented in autoencoder neural networks and learned using squared error plus the same regularization term. We introduce a new model for static data, known as sensible principal component analysis, as well as a novel concept of spatially adaptive observation noise. We also review some of the literature involving global and local mixtures of the basic models and provide pseudocode for inference and learning for all the basic models
Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)
We introduce a new structured kernel interpolation (SKI) framework, which
generalises and unifies inducing point methods for scalable Gaussian processes
(GPs). SKI methods produce kernel approximations for fast computations through
kernel interpolation. The SKI framework clarifies how the quality of an
inducing point approach depends on the number of inducing (aka interpolation)
points, interpolation strategy, and GP covariance kernel. SKI also provides a
mechanism to create new scalable kernel methods, through choosing different
kernel interpolation strategies. Using SKI, with local cubic kernel
interpolation, we introduce KISS-GP, which is 1) more scalable than inducing
point alternatives, 2) naturally enables Kronecker and Toeplitz algebra for
substantial additional gains in scalability, without requiring any grid data,
and 3) can be used for fast and expressive kernel learning. KISS-GP costs O(n)
time and storage for GP inference. We evaluate KISS-GP for kernel matrix
approximation, kernel learning, and natural sound modelling.Comment: 19 pages, 4 figure
Multi-Target Prediction: A Unifying View on Problems and Methods
Multi-target prediction (MTP) is concerned with the simultaneous prediction
of multiple target variables of diverse type. Due to its enormous application
potential, it has developed into an active and rapidly expanding research field
that combines several subfields of machine learning, including multivariate
regression, multi-label classification, multi-task learning, dyadic prediction,
zero-shot learning, network inference, and matrix completion. In this paper, we
present a unifying view on MTP problems and methods. First, we formally discuss
commonalities and differences between existing MTP problems. To this end, we
introduce a general framework that covers the above subfields as special cases.
As a second contribution, we provide a structured overview of MTP methods. This
is accomplished by identifying a number of key properties, which distinguish
such methods and determine their suitability for different types of problems.
Finally, we also discuss a few challenges for future research
A New Distribution-Free Concept for Representing, Comparing, and Propagating Uncertainty in Dynamical Systems with Kernel Probabilistic Programming
This work presents the concept of kernel mean embedding and kernel
probabilistic programming in the context of stochastic systems. We propose
formulations to represent, compare, and propagate uncertainties for fairly
general stochastic dynamics in a distribution-free manner. The new tools enjoy
sound theory rooted in functional analysis and wide applicability as
demonstrated in distinct numerical examples. The implication of this new
concept is a new mode of thinking about the statistical nature of uncertainty
in dynamical systems
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