40,125 research outputs found
Conditional Restricted Boltzmann Machines for Structured Output Prediction
Conditional Restricted Boltzmann Machines (CRBMs) are rich probabilistic
models that have recently been applied to a wide range of problems, including
collaborative filtering, classification, and modeling motion capture data.
While much progress has been made in training non-conditional RBMs, these
algorithms are not applicable to conditional models and there has been almost
no work on training and generating predictions from conditional RBMs for
structured output problems. We first argue that standard Contrastive
Divergence-based learning may not be suitable for training CRBMs. We then
identify two distinct types of structured output prediction problems and
propose an improved learning algorithm for each. The first problem type is one
where the output space has arbitrary structure but the set of likely output
configurations is relatively small, such as in multi-label classification. The
second problem is one where the output space is arbitrarily structured but
where the output space variability is much greater, such as in image denoising
or pixel labeling. We show that the new learning algorithms can work much
better than Contrastive Divergence on both types of problems
Predictive PAC Learning and Process Decompositions
We informally call a stochastic process learnable if it admits a
generalization error approaching zero in probability for any concept class with
finite VC-dimension (IID processes are the simplest example). A mixture of
learnable processes need not be learnable itself, and certainly its
generalization error need not decay at the same rate. In this paper, we argue
that it is natural in predictive PAC to condition not on the past observations
but on the mixture component of the sample path. This definition not only
matches what a realistic learner might demand, but also allows us to sidestep
several otherwise grave problems in learning from dependent data. In
particular, we give a novel PAC generalization bound for mixtures of learnable
processes with a generalization error that is not worse than that of each
mixture component. We also provide a characterization of mixtures of absolutely
regular (-mixing) processes, of independent probability-theoretic
interest.Comment: 9 pages, accepted in NIPS 201
Graphs in machine learning: an introduction
Graphs are commonly used to characterise interactions between objects of
interest. Because they are based on a straightforward formalism, they are used
in many scientific fields from computer science to historical sciences. In this
paper, we give an introduction to some methods relying on graphs for learning.
This includes both unsupervised and supervised methods. Unsupervised learning
algorithms usually aim at visualising graphs in latent spaces and/or clustering
the nodes. Both focus on extracting knowledge from graph topologies. While most
existing techniques are only applicable to static graphs, where edges do not
evolve through time, recent developments have shown that they could be extended
to deal with evolving networks. In a supervised context, one generally aims at
inferring labels or numerical values attached to nodes using both the graph
and, when they are available, node characteristics. Balancing the two sources
of information can be challenging, especially as they can disagree locally or
globally. In both contexts, supervised and un-supervised, data can be
relational (augmented with one or several global graphs) as described above, or
graph valued. In this latter case, each object of interest is given as a full
graph (possibly completed by other characteristics). In this context, natural
tasks include graph clustering (as in producing clusters of graphs rather than
clusters of nodes in a single graph), graph classification, etc. 1 Real
networks One of the first practical studies on graphs can be dated back to the
original work of Moreno [51] in the 30s. Since then, there has been a growing
interest in graph analysis associated with strong developments in the modelling
and the processing of these data. Graphs are now used in many scientific
fields. In Biology [54, 2, 7], for instance, metabolic networks can describe
pathways of biochemical reactions [41], while in social sciences networks are
used to represent relation ties between actors [66, 56, 36, 34]. Other examples
include powergrids [71] and the web [75]. Recently, networks have also been
considered in other areas such as geography [22] and history [59, 39]. In
machine learning, networks are seen as powerful tools to model problems in
order to extract information from data and for prediction purposes. This is the
object of this paper. For more complete surveys, we refer to [28, 62, 49, 45].
In this section, we introduce notations and highlight properties shared by most
real networks. In Section 2, we then consider methods aiming at extracting
information from a unique network. We will particularly focus on clustering
methods where the goal is to find clusters of vertices. Finally, in Section 3,
techniques that take a series of networks into account, where each network i
Gibbs Max-margin Topic Models with Data Augmentation
Max-margin learning is a powerful approach to building classifiers and
structured output predictors. Recent work on max-margin supervised topic models
has successfully integrated it with Bayesian topic models to discover
discriminative latent semantic structures and make accurate predictions for
unseen testing data. However, the resulting learning problems are usually hard
to solve because of the non-smoothness of the margin loss. Existing approaches
to building max-margin supervised topic models rely on an iterative procedure
to solve multiple latent SVM subproblems with additional mean-field assumptions
on the desired posterior distributions. This paper presents an alternative
approach by defining a new max-margin loss. Namely, we present Gibbs max-margin
supervised topic models, a latent variable Gibbs classifier to discover hidden
topic representations for various tasks, including classification, regression
and multi-task learning. Gibbs max-margin supervised topic models minimize an
expected margin loss, which is an upper bound of the existing margin loss
derived from an expected prediction rule. By introducing augmented variables
and integrating out the Dirichlet variables analytically by conjugacy, we
develop simple Gibbs sampling algorithms with no restricting assumptions and no
need to solve SVM subproblems. Furthermore, each step of the
"augment-and-collapse" Gibbs sampling algorithms has an analytical conditional
distribution, from which samples can be easily drawn. Experimental results
demonstrate significant improvements on time efficiency. The classification
performance is also significantly improved over competitors on binary,
multi-class and multi-label classification tasks.Comment: 35 page
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