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Machine learning phases in statistical physics
Conventionally, the study of phases in statistical mechan- ics is performed with the help of random sampling tools. Among the most powerful are Monte Carlo simulations consisting of a stochastic importance sampling over state space and evaluation of estimators for physical quantities. The ability of modern machine learning techniques to classify, identify, or in- terpret massive data sets provides a complementary paradigm to the above approach to analyze the exponentially large number of states in statistical physics. In this report, it is demonstrated by application on Ising-type models that deep learning has potential wide applications in solving many-body statis- tical physics problems. In application of supervised learning, we showed that the feed-forward neural network can identify phases and phase transitions in the ferromagnetic Ising model and the convolutional neural network (CNN) is extremely powerful in classifying T = 0 and T = ∞ phases in the Ising gauge model; In application of unsupervised learning, we illustrated that a deep auto-encoder constructed by stacked restricted Boltzmann machines (RBM)
is closely related to the renormalization group (RG) method well understood in modern physics and our reconstruction of Ising spin configurations in the ferromagnetic Ising model is similar to the hand-written digits reconstruction.Statistic
DeepCoder: Semi-parametric Variational Autoencoders for Automatic Facial Action Coding
Human face exhibits an inherent hierarchy in its representations (i.e.,
holistic facial expressions can be encoded via a set of facial action units
(AUs) and their intensity). Variational (deep) auto-encoders (VAE) have shown
great results in unsupervised extraction of hierarchical latent representations
from large amounts of image data, while being robust to noise and other
undesired artifacts. Potentially, this makes VAEs a suitable approach for
learning facial features for AU intensity estimation. Yet, most existing
VAE-based methods apply classifiers learned separately from the encoded
features. By contrast, the non-parametric (probabilistic) approaches, such as
Gaussian Processes (GPs), typically outperform their parametric counterparts,
but cannot deal easily with large amounts of data. To this end, we propose a
novel VAE semi-parametric modeling framework, named DeepCoder, which combines
the modeling power of parametric (convolutional) and nonparametric (ordinal
GPs) VAEs, for joint learning of (1) latent representations at multiple levels
in a task hierarchy1, and (2) classification of multiple ordinal outputs. We
show on benchmark datasets for AU intensity estimation that the proposed
DeepCoder outperforms the state-of-the-art approaches, and related VAEs and
deep learning models.Comment: ICCV 2017 - accepte
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