Using online linear classifiers to filter spam Emails

The performance of two online linear classifiers - the Perceptron and Littlestone’s Winnow – is explored for two anti-spam filtering benchmark corpora - PU1 and Ling-Spam. We study the performance for varying numbers of features, along with three different feature selection methods: Information Gain (IG), Document Frequency (DF) and Odds Ratio. The size of the training set and the number of training iterations are also investigated for both classifiers. The experimental results show that both the Perceptron and Winnow perform much better when using IG or DF than using Odds Ratio. It is further demonstrated that when using IG or DF, the classifiers are insensitive to the number of features and the number of training iterations, and not greatly sensitive to the size of training set. Winnow is shown to slightly outperform the Perceptron. It is also demonstrated that both of these online classifiers perform much better than a standard Naïve Bayes method. The theoretical and implementation computational complexity of these two classifiers are very low, and they are very easily adaptively updated. They outperform most of the published results, while being significantly easier to train and adapt. The analysis and promising experimental results indicate that the Perceptron and Winnow are two very competitive classifiers for anti-spam filtering

Parallel strategy for optimal learning in perceptrons

We developed a parallel strategy for learning optimally specific realizable rules by perceptrons, in an online learning scenario. Our result is a generalization of the Caticha–Kinouchi (CK) algorithm developed for learning a perceptron with a synaptic vector drawn from a uniform distribution over the N-dimensional sphere, so called the typical case. Our method outperforms the CK algorithm in almost all possible situations, failing only in a denumerable set of cases. The algorithm is optimal in the sense that it saturates Bayesian bounds when it succeeds

Generalizing with perceptrons in case of structured phase- and pattern-spaces

We investigate the influence of different kinds of structure on the learning behaviour of a perceptron performing a classification task defined by a teacher rule. The underlying pattern distribution is permitted to have spatial correlations. The prior distribution for the teacher coupling vectors itself is assumed to be nonuniform. Thus classification tasks of quite different difficulty are included. As learning algorithms we discuss Hebbian learning, Gibbs learning, and Bayesian learning with different priors, using methods from statistics and the replica formalism. We find that the Hebb rule is quite sensitive to the structure of the actual learning problem, failing asymptotically in most cases. Contrarily, the behaviour of the more sophisticated methods of Gibbs and Bayes learning is influenced by the spatial correlations only in an intermediate regime of $\alpha$, where $\alpha$ specifies the size of the training set. Concerning the Bayesian case we show, how enhanced prior knowledge improves the performance.Comment: LaTeX, 32 pages with eps-figs, accepted by J Phys

On the role of synaptic stochasticity in training low-precision neural networks

Stochasticity and limited precision of synaptic weights in neural network models are key aspects of both biological and hardware modeling of learning processes. Here we show that a neural network model with stochastic binary weights naturally gives prominence to exponentially rare dense regions of solutions with a number of desirable properties such as robustness and good generalization performance, while typical solutions are isolated and hard to find. Binary solutions of the standard perceptron problem are obtained from a simple gradient descent procedure on a set of real values parametrizing a probability distribution over the binary synapses. Both analytical and numerical results are presented. An algorithmic extension aimed at training discrete deep neural networks is also investigated.Comment: 7 pages + 14 pages of supplementary materia

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

Constructive Preference Elicitation over Hybrid Combinatorial Spaces

Preference elicitation is the task of suggesting a highly preferred configuration to a decision maker. The preferences are typically learned by querying the user for choice feedback over pairs or sets of objects. In its constructive variant, new objects are synthesized "from scratch" by maximizing an estimate of the user utility over a combinatorial (possibly infinite) space of candidates. In the constructive setting, most existing elicitation techniques fail because they rely on exhaustive enumeration of the candidates. A previous solution explicitly designed for constructive tasks comes with no formal performance guarantees, and can be very expensive in (or unapplicable to) problems with non-Boolean attributes. We propose the Choice Perceptron, a Perceptron-like algorithm for learning user preferences from set-wise choice feedback over constructive domains and hybrid Boolean-numeric feature spaces. We provide a theoretical analysis on the attained regret that holds for a large class of query selection strategies, and devise a heuristic strategy that aims at optimizing the regret in practice. Finally, we demonstrate its effectiveness by empirical evaluation against existing competitors on constructive scenarios of increasing complexity.Comment: AAAI 2018, computing methodologies, machine learning, learning paradigms, supervised learning, structured output