1,721,083 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
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
New perspectives in computational intelligence: nothing so intelligent as randomness, nothing so effective as asymmetry
No full textLeaving the expert systems framework of the 80s and the early connectionist paradigm of the 90s, the scientific community is now drawn by social computing paradigms, where a huge number of agents individually do an
elementary job and jointly give rise to a sophisticated functionality. There is no
doubt that the complexity of this functionality is connected to the randomness
of the agents’ work. What comes increasingly clear is that this randomness is a guarantee of success, not a drawback, provided we avoid falling in the ordinary Gaussian phenomenology in the province of the central limit theorem. We envisage a jointly biased asymmetry of the agents’ actions to be the main feature distinguishing them from the molecules of a gas in Brownian motion,
and toss this idea in the paper through specific statistical models we elaborated
in recent works
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
A New Goodness-Of-Fit Statistical Test
No full textWe introduce a new concept of nonparametric test for statistically deciding if a model fits a sample of data well. The employed statistic is the empirical cumulative distribution (e.c.d.f.) of the measure of the blocks determined by the ordered sample. For any distribution law underlying the data this statistic is distributed around a Beta cumulative distribution law (c.d.f.) so that the shift between the two curves is the statistic at the basis of the test. Its distribution is computed through a new bootstrap procedure from a population of free parameters of the model that are compatible with the sampled data according to the model. Closing the loop, we may expect that if the model fits the data well the Beta c.d.f. constitutes a template for the block e.c.d.f.s that are compatible with the observed data. In the paper we show how to appreciate the template functionality in the case of a good fit and also how to discriminate bad models. We show the test's potential in comparison to conventional tests, both in case studies and in a well-known benchmark for the semiparametric logistic model used widely in database analysis
Algorithmic inference approach to learn copulas
No full textWe introduce a new method for estimating the parameter α of the Clayton copulas
within the framework of Algorithmic Inference. The method consists of a variant
of the standard bootstrapping procedure for inferring random parameters, which
we expressly devise to bypass the two pitfalls of this specific instance: the non
independence of the Kendall statistics, customary at the basis of this inference
task, and the absence of a sufficient statistic w.r.t. α. The variant is rooted on a
numerical procedure in order to find the α estimate at a fixed point of an iterative
routine. Numerical results show a good accuracy of the estimates, though paired
in some cases with the complexity of the programs which compute them
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
Identifying elementary iterated systems through algorithmic inference : The Cantor set example
No full textWe come back to the old problem of fractal identification within the new framework of algorithmic Inference. The key points are: (i) to identify sufficient statistics to be put in connection with the unknown values of the fractal parameters, and (ii) to manage the timing of the iterated process through spatial statistics. We fill these tasks successfully with the Cantor sets. We are able to compute confidence intervals for both the scaling parameter theta and the iteration number n at which we are observing a set. We both check numerically the coverage of these intervals and delineate a general strategy for affording more complex iterated systems
Discovering regression data quality through clustering methods
No full textWe propose the use of clustering methods in order to discover the quality of each element in a training set to be subsequently fed to a regression algorithm. The paper shows that these methods, used in combination with regression algorithms taking into account the additional information conveyed by this kind of quality, allow the attainment of higher performances than those obtained through standard techniques
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