13 research outputs found
Learning Representations by Maximizing Compression
We give an algorithm that learns a representation of data through
compression. The algorithm 1) predicts bits sequentially from those previously
seen and 2) has a structure and a number of computations similar to an
autoencoder. The likelihood under the model can be calculated exactly, and
arithmetic coding can be used directly for compression. When training on digits
the algorithm learns filters similar to those of restricted boltzman machines
and denoising autoencoders. Independent samples can be drawn from the model by
a single sweep through the pixels. The algorithm has a good compression
performance when compared to other methods that work under random ordering of
pixels.Comment: 8 pages, 3 figure
Herding as a Learning System with Edge-of-Chaos Dynamics
Herding defines a deterministic dynamical system at the edge of chaos. It
generates a sequence of model states and parameters by alternating parameter
perturbations with state maximizations, where the sequence of states can be
interpreted as "samples" from an associated MRF model. Herding differs from
maximum likelihood estimation in that the sequence of parameters does not
converge to a fixed point and differs from an MCMC posterior sampling approach
in that the sequence of states is generated deterministically. Herding may be
interpreted as a"perturb and map" method where the parameter perturbations are
generated using a deterministic nonlinear dynamical system rather than randomly
from a Gumbel distribution. This chapter studies the distinct statistical
characteristics of the herding algorithm and shows that the fast convergence
rate of the controlled moments may be attributed to edge of chaos dynamics. The
herding algorithm can also be generalized to models with latent variables and
to a discriminative learning setting. The perceptron cycling theorem ensures
that the fast moment matching property is preserved in the more general
framework
Representation Learning: A Review and New Perspectives
The success of machine learning algorithms generally depends on data
representation, and we hypothesize that this is because different
representations can entangle and hide more or less the different explanatory
factors of variation behind the data. Although specific domain knowledge can be
used to help design representations, learning with generic priors can also be
used, and the quest for AI is motivating the design of more powerful
representation-learning algorithms implementing such priors. This paper reviews
recent work in the area of unsupervised feature learning and deep learning,
covering advances in probabilistic models, auto-encoders, manifold learning,
and deep networks. This motivates longer-term unanswered questions about the
appropriate objectives for learning good representations, for computing
representations (i.e., inference), and the geometrical connections between
representation learning, density estimation and manifold learning
Stochastic Spectral Descent for Discrete Graphical Models
Interest in deep probabilistic graphical models has increased in recent years, due to their state-of-the-art perfor- mance on many machine learning applications. Such models are typically trained with the stochastic gradient method, which can take a significant number of iterations to converge. Since the computational cost of gradient estimation is prohibitive even for modestly-sized models, training becomes slow and practically- usable models are kept small. In this paper we propose a new, largely tuning-free algorithm to address this problem. Our approach derives novel majorization bounds based on the Schatten-∞ norm. Intriguingly, the minimizers of these bounds can be interpreted as gradient methods in a non-Euclidean space. We thus propose using a stochastic gradient method in non-Euclidean space. We both provide simple conditions under which our algorithm is guaranteed to converge, and demonstrate empirically that our algorithm leads to dramatically faster training and improved predictive ability compared to stochastic gradient descent for both directed and undirected graphical models