Confidence About Possible Explanations.

We revise the notion of confidence with which we estimate the parameters of a given distribution law in terms of their compatibility with the sample we have observed. This is a recent perspective that allows us to get a more intuitive feeling of the crucial concept of the confidence interval in parametric inference together with quick tools for exactly computing them even in conditions far from the common Gaussian framework where standard methods fail. The key artifact consists of working with a representation of the compatible parameters in terms of random variables without priors. This leads to new estimators that meet the most demanding requirements of the modern statistical inference in terms of learning algorithms. We support our methods with: a consistent theoretical framework, general-purpose estimation procedures, and a set of paradigmatic benchmarks.

Appreciation of medical treatments through confidence intervals.

The typical way of judging about either the efficacy of a new treatment or, on the contrary, the damage of a pollutant agent is through a test of hypothesis having its ineffectiveness as null hypothesis. This is the typical operational field of Kolmogorov's statistical framework where wastes of data (for instance non significant deaths in a polluted region) represent the main drawback. Instead, confidence intervals about treatment/pollution effectiveness are a way of exploiting all data, whatever their number is. We recently proposed a new statistical framework, called Algorithmic Inference, for overcoming crucial difficulties usually met when computing these intervals and abandoning general simplifying hypotheses such as errors' Gaussian distribution. When effectiveness is expressed in terms of regression curves between observed data we come to a learning problem that we solve by identifying a region where the whole curve lies with a given confidence. The approach to inference we propose is very suitable for identifying these regions with great accuracy, even in the case of nonlinear regression models and/or a limited size of the observed sample, provided that a normally powered computing station is available. In the paper we discuss this new way of extracting functions from the experimental data and drawing conclusions about the treatments originating them. From an operational perspective, we give the general layout of the procedure for computing confidence regions as well as some applications on real data.

DNA fragment assembly using neural prediction techniques.

The paper describes an alternative approach to the fragment assembly problem. The key idea is to train a recurrent neural network to tracking the sequence of bases constituting a given fragment and to assign to a same cluster all the sequences which are well tracked by this network. We make use of a 3-layer Recurrent Perceptron and examine both edited sequences from a ftp site and artificial fragments from a common simulation software: the clusters we obtain exhibit interesting properties in terms of error filtering, stability and self consistency; we define as well, with a certain degree of approximation, a metric on the fragment set. The proposed assembly algorithm is susceptible to becoming an alternative method with the following properties: (i) high quality of the rebuilt genomic sequences, (ii) high parallelizability of the computing process with consequent drastic reduction of the running time.

Sub-symbolically managing pieces of symbolical functions for sorting.

We present a hybrid system for managing both symbolic and subsymbolic knowledge in a uniform way. Our aim is to solve problems where some gap in formal theories occurs which stops us from getting a fully symbolical solution. The idea is to use neural modules to functionally connect pieces of symbolical knowledge, such as mathematical formulas and deductive rules. The whole system is trained through a backpropagation learning algorithm where all (symbolic or subsymbolic) free parameters are updated piping back the error through each component of the system. The structure of this system is very general, possibly varying over time, possibly managing fuzzy variables and decision trees. We use as a test-bed the problem of sorting a file, where suitable suggestions on next sorting moves are supplied by the network also on the basis of hints provided by some conventional sorters. A comprehensive discussion of system performance is provided in order to understand behaviors and capabilities of the proposed hybrid system.

Asymmetric Boltzmann machines.

We study asymmetric stochastic networks from two points of view: combinatorial optimization and learning algorithms based on relative entropy minimization. We show that there are non trivial classes of asymmetric networks which admit a Lyapunov function L under deterministic parallel evolution and prove that the stochastic augmentation of such networks amounts to a stochastic search for global minima of L. The problem of minimizing L for a totally antisymmetric parallel network is shown to be associated to an NP-complete decision problem. The study of entropic learning for general asymmetric networks, performed in the non equilibrium, time dependent formalism, leads to a Hebbian rule based on time averages over the past history of the system. The general algorithm for asymmetric networks is tested on a feed-forward architecture.