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Weight Priors for Learning Identity Relations
Learning abstract and systematic relations has been an open issue in neural network learning for over 30 years. It has been shown recently that neural networks do not learn relations based on identity and are unable to generalize well to unseen data. The Relation Based Pattern (RBP) approach has been proposed as a solution for this problem. In this work, we extend RBP by realizing it as a Bayesian prior on network weights to model the identity relations. This weight prior leads to a modified regularization term in otherwise standard network learning. In our experiments, we show that the Bayesian weight priors lead to perfect generalization when learning identity based relations and do not impede general neural network learning. We believe that the approach of creating an inductive bias with weight priors can be extended easily to other forms of relations and will be beneficial for many other learning tasks
Bayesian Networks Optimization Based on Induction Learning Techniques
Abstract Obtaining a bayesian network from data is a learning process that is divided in two steps: structural learning and parametric learning. In this paper, we define an automatic learning method that optimizes the bayesian networks applied to classification, using a hybrid method of learning that combines the advantages of the induction techniques of the decision trees with those of the bayesian networks
The Neural Particle Filter
The robust estimation of dynamically changing features, such as the position
of prey, is one of the hallmarks of perception. On an abstract, algorithmic
level, nonlinear Bayesian filtering, i.e. the estimation of temporally changing
signals based on the history of observations, provides a mathematical framework
for dynamic perception in real time. Since the general, nonlinear filtering
problem is analytically intractable, particle filters are considered among the
most powerful approaches to approximating the solution numerically. Yet, these
algorithms prevalently rely on importance weights, and thus it remains an
unresolved question how the brain could implement such an inference strategy
with a neuronal population. Here, we propose the Neural Particle Filter (NPF),
a weight-less particle filter that can be interpreted as the neuronal dynamics
of a recurrently connected neural network that receives feed-forward input from
sensory neurons and represents the posterior probability distribution in terms
of samples. Specifically, this algorithm bridges the gap between the
computational task of online state estimation and an implementation that allows
networks of neurons in the brain to perform nonlinear Bayesian filtering. The
model captures not only the properties of temporal and multisensory integration
according to Bayesian statistics, but also allows online learning with a
maximum likelihood approach. With an example from multisensory integration, we
demonstrate that the numerical performance of the model is adequate to account
for both filtering and identification problems. Due to the weightless approach,
our algorithm alleviates the 'curse of dimensionality' and thus outperforms
conventional, weighted particle filters in higher dimensions for a limited
number of particles
Reasoning about Independence in Probabilistic Models of Relational Data
We extend the theory of d-separation to cases in which data instances are not
independent and identically distributed. We show that applying the rules of
d-separation directly to the structure of probabilistic models of relational
data inaccurately infers conditional independence. We introduce relational
d-separation, a theory for deriving conditional independence facts from
relational models. We provide a new representation, the abstract ground graph,
that enables a sound, complete, and computationally efficient method for
answering d-separation queries about relational models, and we present
empirical results that demonstrate effectiveness.Comment: 61 pages, substantial revisions to formalisms, theory, and related
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Optimization and Abstraction: A Synergistic Approach for Analyzing Neural Network Robustness
In recent years, the notion of local robustness (or robustness for short) has
emerged as a desirable property of deep neural networks. Intuitively,
robustness means that small perturbations to an input do not cause the network
to perform misclassifications. In this paper, we present a novel algorithm for
verifying robustness properties of neural networks. Our method synergistically
combines gradient-based optimization methods for counterexample search with
abstraction-based proof search to obtain a sound and ({\delta}-)complete
decision procedure. Our method also employs a data-driven approach to learn a
verification policy that guides abstract interpretation during proof search. We
have implemented the proposed approach in a tool called Charon and
experimentally evaluated it on hundreds of benchmarks. Our experiments show
that the proposed approach significantly outperforms three state-of-the-art
tools, namely AI^2 , Reluplex, and Reluval
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