A tutorial on energy-based learning

Probabilistic graphical models associate a probability to each configuration of the relevant variables. Energy-based models (EBM) associate an energy to those configurations, eliminating the need for proper normalization of probability distributions. Making a decision (an inference) with an EBM consists in comparing the energies associated with various configurations of the variable to be predicted, and choosing the one with the smallest energy. Such systems must be trained discriminatively to associate low energies to the desired configurations and higher energies to undesired configurations. A wide variety of loss function can be used for this purpose. We give sufficient conditions that a loss function should satisfy so that its minimization will cause the system to approach to desired behavior. We give many specific examples of suitable loss functions, and show an application to object recognition in images. it is important to note that the energy is quantity minimized

2008

Abstract In this paper we propose an energy-based model (EBM) for selecting subsets of features that are both causally and predictively relevant for classification tasks. The proposed method is tested in the causality challenge, a competition that promotes research on strengthen feature selection by taking into account causal information of features.

2013

Editor: Isabelle Guyon et al. In this paper we propose an energy-based model (EBM) for selecting subsets of features that are both causally and predictively relevant for classification tasks. The proposed method is tested in the causality challenge, a competition that promotes research on strengthen feature selection by taking into account causal information of features. Under the proposed approach, an energy value is assigned to every configuration of features and the problem is reduced to that of finding the configuration that minimizes an energy function. We propose an energy function that takes into account causal, predictive, and relevance/correlation information of features. Particularly, we introduce potentials that combine the rankings of individual feature selection methods, Markov blanket information and predictive performance estimations. The configuration with lower energy will be that offering the best tradeoff between these sources of information. Experimental results ...

We introduce a view of unsupervised learning that integrates probabilistic and nonprobabilistic methods for clustering, dimensionality reduction, and feature extraction in a unified framework. In this framework, an energy function associates low energies to input points that are similar to training samples, and high energies to unobserved points. Learning consists in minimizing the energies of training samples while ensuring that the energies of unobserved ones are higher. Some traditional methods construct the architecture so that only a small number of points can have low energy, while other methods explicitly "pull up" on the energies of unobserved points. In probabilistic methods the energy of unobserved points is pulled by minimizing the log partition function, an expensive, and sometimes intractable process. We explore different and more efficient methods using an energy-based approach. In particular, we show that a simple solution is to restrict the amount of information contained in codes that represent the data. We demonstrate such a method by training it on natural image patches and by applying to image denoising.

to describe supervised and unsupervised training methods for probabilistic and non-probabilistic factor graphs. An energy-based model associates a scalar energy to configurations of inputs, outputs, and latent variables. Inference consists in finding configurations of output and latent variables that minimize the energy. Learning consists in finding parameters that minimize a suitable loss function so that the module produces lower energies for "correct" outputs than for all "incorrect" outputs. Learning machines can be constructed by assembling modules and loss functions. Gradient-based learning procedures are easily implemented through semi-automatic differentiation of complex models constructed by assembling predefined modules. We introduce an open-source and cross-platform C++ library called EBLearn 1 to enable the construction of energy-based learning models. EBLearn is composed of two major components, libidx: an efficient and very flexible multi-dimensional tensor library, and libeblearn: an object-oriented library of trainable modules and learning algorithms. The latter has facilities for such models as convolutional networks, as well as for image processing. It also provides graphical display functions.

Neural Computation, 2003

We study the selectivity properties of neurons based on BCM and kurtosis energy functions in a general case of noisy high-dimensional input space. The proposed approach, which is used for characterization of the stable states, can be generalized to a whole class of energy functions. We characterize the critical noise levels beyond which the selectivity is destroyed. We also perform a quantitative analysis of such transitions, which shows interesting dependency on data set size. We observe that the robustness to noise of the BCM neuron (Bienenstock, Cooper, & Munro, 1982; Intrator & Cooper, 1992) increases as a function of dimensionality. We explicitly compute the separability limit of BCM and kurtosis learning rules in the case of a bimodal input distribution. Numerical simulations show a stronger robustness of the BCM rule for practical data set size when compared with kurtosis.

Proceedings of the 3rd International Conference on Future Energy Systems Where Energy, Computing and Communication Meet - e-Energy '12, 2012

In this paper we describe an ongoing project which develops an automated residential Demand Response (DR) system that attempts to manage residential loads in accordance with DR signals. In this early stage of the project, we propose an approach for identifying individual appliance consumption from the aggregate load and discuss the effectiveness of load disaggregation techniques when total load data also includes appliances that are unmonitored even during the training phase. We show that simple discriminative methods can directly predict the appliance states (e.g. on, off, standby) and the predicted state can be used to calculate energy consumed by the appliances. We also show that these methods perform substantially better than the generative models of energy consumption that are commonly used. We evaluated the proposed approach using publicly available REDD data set, and our experimental evaluation demonstrates the improvement in accuracy.

Phys. Chem. Chem. Phys., 2017

The energy landscapes framework developed in molecular science provides new insight in the field of machine learning.

Machine learning techniques are being increasingly used as flexible non-linear fitting and prediction tools in the physical sciences. Fitting functions that exhibit multiple solutions as local minima can be analysed in terms of the corresponding machine learning landscape. Methods to explore and visualise molecular potential energy landscapes can be applied to these machine learning landscapes to gain new insight into the solution space involved in training and the nature of the corresponding predictions. In particular, we can define quantities analogous to molecular structure, thermodynamics, and kinetics, and relate these emergent properties to the structure of the underlying landscape. This Perspective aims to describe these analogies with examples from recent applications, and suggest avenues for new interdisciplinary research.

Complex behavior is supported by the coordination of multiple brain regions. We propose coordination is achieved by a controller-peripheral architecture in which peripherals (e.g., the ventral visual stream) aim to supply needed inputs to their controllers (e.g., the hippocampus and prefrontal cortex) while expending minimal resources. We developed a formal model within this frame-work to address how multiple brain regions coordinate to support rapid learning from a few example images. The model captured how higher-level activity in the controller shaped lower-level visual representations, affecting their precision and sparsity in a manner that paralleled brain measures. Alternative models optimized by gradient descent irrespective of architectural constraints could not account for human behavior or brain responses, and, typical of standard deep learning approaches, were unstable trial-by-trial learners.