12,820 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
A self-learning algorithm for biased molecular dynamics
A new self-learning algorithm for accelerated dynamics, reconnaissance
metadynamics, is proposed that is able to work with a very large number of
collective coordinates. Acceleration of the dynamics is achieved by
constructing a bias potential in terms of a patchwork of one-dimensional,
locally valid collective coordinates. These collective coordinates are obtained
from trajectory analyses so that they adapt to any new features encountered
during the simulation. We show how this methodology can be used to enhance
sampling in real chemical systems citing examples both from the physics of
clusters and from the biological sciences.Comment: 6 pages, 5 figures + 9 pages of supplementary informatio
Probabilistic Inference from Arbitrary Uncertainty using Mixtures of Factorized Generalized Gaussians
This paper presents a general and efficient framework for probabilistic
inference and learning from arbitrary uncertain information. It exploits the
calculation properties of finite mixture models, conjugate families and
factorization. Both the joint probability density of the variables and the
likelihood function of the (objective or subjective) observation are
approximated by a special mixture model, in such a way that any desired
conditional distribution can be directly obtained without numerical
integration. We have developed an extended version of the expectation
maximization (EM) algorithm to estimate the parameters of mixture models from
uncertain training examples (indirect observations). As a consequence, any
piece of exact or uncertain information about both input and output values is
consistently handled in the inference and learning stages. This ability,
extremely useful in certain situations, is not found in most alternative
methods. The proposed framework is formally justified from standard
probabilistic principles and illustrative examples are provided in the fields
of nonparametric pattern classification, nonlinear regression and pattern
completion. Finally, experiments on a real application and comparative results
over standard databases provide empirical evidence of the utility of the method
in a wide range of applications
Automatic Differentiation Variational Inference
Probabilistic modeling is iterative. A scientist posits a simple model, fits
it to her data, refines it according to her analysis, and repeats. However,
fitting complex models to large data is a bottleneck in this process. Deriving
algorithms for new models can be both mathematically and computationally
challenging, which makes it difficult to efficiently cycle through the steps.
To this end, we develop automatic differentiation variational inference (ADVI).
Using our method, the scientist only provides a probabilistic model and a
dataset, nothing else. ADVI automatically derives an efficient variational
inference algorithm, freeing the scientist to refine and explore many models.
ADVI supports a broad class of models-no conjugacy assumptions are required. We
study ADVI across ten different models and apply it to a dataset with millions
of observations. ADVI is integrated into Stan, a probabilistic programming
system; it is available for immediate use
Topic-based mixture language modelling
This paper describes an approach for constructing a mixture of language models based on simple statistical notions of semantics using probabilistic models developed for information retrieval. The approach encapsulates corpus-derived semantic information and is able to model varying styles of text. Using such information, the corpus texts are clustered in an unsupervised manner and a mixture of topic-specific language models is automatically created. The principal contribution of this work is to characterise the document space resulting from information retrieval techniques and to demonstrate the approach for mixture language modelling.
A comparison is made between manual and automatic clustering in order to elucidate how the global content information is expressed in the space. We also compare (in terms of association with manual clustering and language modelling accuracy) alternative term-weighting schemes and the effect of singular value decomposition dimension reduction (latent semantic analysis). Test set perplexity results using the British National Corpus indicate that the approach can improve the potential of statistical language modelling. Using an adaptive procedure, the conventional model may be tuned to track text data with a slight increase in computational cost
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