451 research outputs found
Regressing data with independent parameters
No full textWithin the framework of Algorithmic Inference, we recall a linear regression analysis tool based on the identification of the joint probability distribution of the regression coefficients compatible with the sampled data and aimed at finding out the independent components of this distribution. On this distribution we implement specific Independent Component Analysis (ICA) procedures to obtain the parameter independent components giving rise to suitable confidence regions also when the noise term is far from being independent and identically Gaussian
Toward a cooperative brain: Continuing the work with John Taylor
No full textI propose a three-step discussion following a research path shared in part with John Taylor where the leitmotif is to understand the cooperation between thinking agents: the pRAM architecture, the butler paradigm, and the networked intelligence. All three steps comprise keystones of European projects which one of us has coordinated. The principled philosophy is to 'start simple and insert progressive complexity'. The results I discuss only go as far as the 'start simple' point. The final goal is to find a bias that underpins the entire research effort. In this paper I will move within the connectionist paradigm at various scales, the largest being one that encompasses an Internet of Things instantiation. © 2013 IEEE
Sources of asymmetric randomness
No full textIn view of discussing the genuine roots of the connectionist paradigm we toss in this paper the non symmetry features of the involved random phenomena. Reading these features in terms of intentionality with which we drive a learning process far from a simple random walk, we focus on elementary processes where trajectories cannot be decomposed as the sum of a deterministic recursive function plus a symmetric noise. Rather we look at nonlinear compositions of the above ingredients, as a source of genuine non symmetric atomic random actions, like those at the basis of a training process. To this aim we introduce an extended Pareto distribution law with which we analyze some intentional trajectories. With this model we issue some preliminary considerations on elapsed times of training sessions of some families of neural networks
Confidence About Possible Explanations
No full textWe 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
P-sufficient statistics for PAC learning k-term-DNF formulas through enumeration
No full textAbstractWorking in the framework of PAC-learning theory, we present special statistics for accomplishing in polynomial time proper learning of DNF boolean formulas having a fixed number of monomials. Our statistics turn out to be near sufficient for a large family of distribution laws – that we call butterfly distributions. We develop a theory of most powerful learning for analyzing the performance of learning algorithms, with particular reference to trade-offs between power and computational costs. Focusing attention on sample and time complexity, we prove that our algorithm works as efficiently as the best algorithms existing in the literature – while the latter only take care of subclasses of our family of distributions
A feed-forward neural logic based on synaptic and volume transmission
No full textWe consider a homeostatic mechanism to maintain a plastic layer of a feed-forward neural network reactive to a long sequence of signals, with neither falling in a fixed point of the state space nor undergoing in overfitting. Homeostasis is achieved without asking the neural network to be able to pursue an offset through local feedbacks. Rather, each neuron evolves monotonically in the direction increasing its own parameter, while a global feedback emerges from volume transmission of a homostatic signal. Namely: 1) each neuron is triggered to increase its own parameter in order to exceed the mean value of all of the other neurons' parameters, and 2) a global feedback on the population emerges from the composition of the single neurons behavior paired with a reasonable rule through which surrounding neurons in the same layer are activated. We provide a formal description of the model that we implement in an ad hoc version of π-calculus. Some numerical simulations will depict some typical behaviors that seem to show a plausible biological interpretation
- …
