Robust regression with imprecise data

We consider the problem of regression analysis with imprecise data. By imprecise data we mean imprecise observations of precise quantities in the form of sets of values. In this paper, we explore a recently introduced likelihood-based approach to regression with such data. The approach is very general, since it covers all kinds of imprecise data (i.e. not only intervals) and it is not restricted to linear regression. Its result consists of a set of functions, reflecting the entire uncertainty of the regression problem. Here we study in particular a robust special case of the likelihood-based imprecise regression, which can be interpreted as a generalization of the method of least median of squares. Moreover, we apply it to data from a social survey, and compare it with other approaches to regression with imprecise data. It turns out that the likelihood-based approach is the most generally applicable one and is the only approach accounting for multiple sources of uncertainty at the same time

Fair comparison of skin detection approaches on publicly available datasets

Skin detection is the process of discriminating skin and non-skin regions in a digital image and it is widely used in several applications ranging from hand gesture analysis to track body parts and face detection. Skin detection is a challenging problem which has drawn extensive attention from the research community, nevertheless a fair comparison among approaches is very difficult due to the lack of a common benchmark and a unified testing protocol. In this work, we investigate the most recent researches in this field and we propose a fair comparison among approaches using several different datasets. The major contributions of this work are an exhaustive literature review of skin color detection approaches, a framework to evaluate and combine different skin detector approaches, whose source code is made freely available for future research, and an extensive experimental comparison among several recent methods which have also been used to define an ensemble that works well in many different problems. Experiments are carried out in 10 different datasets including more than 10000 labelled images: experimental results confirm that the best method here proposed obtains a very good performance with respect to other stand-alone approaches, without requiring ad hoc parameter tuning. A MATLAB version of the framework for testing and of the methods proposed in this paper will be freely available from https://github.com/LorisNann

Updating beliefs with incomplete observations

Currently, there is renewed interest in the problem, raised by Shafer in 1985, of updating probabilities when observations are incomplete. This is a fundamental problem in general, and of particular interest for Bayesian networks. Recently, Grunwald and Halpern have shown that commonly used updating strategies fail in this case, except under very special assumptions. In this paper we propose a new method for updating probabilities with incomplete observations. Our approach is deliberately conservative: we make no assumptions about the so-called incompleteness mechanism that associates complete with incomplete observations. We model our ignorance about this mechanism by a vacuous lower prevision, a tool from the theory of imprecise probabilities, and we use only coherence arguments to turn prior into posterior probabilities. In general, this new approach to updating produces lower and upper posterior probabilities and expectations, as well as partially determinate decisions. This is a logical consequence of the existing ignorance about the incompleteness mechanism. We apply the new approach to the problem of classification of new evidence in probabilistic expert systems, where it leads to a new, so-called conservative updating rule. In the special case of Bayesian networks constructed using expert knowledge, we provide an exact algorithm for classification based on our updating rule, which has linear-time complexity for a class of networks wider than polytrees. This result is then extended to the more general framework of credal networks, where computations are often much harder than with Bayesian nets. Using an example, we show that our rule appears to provide a solid basis for reliable updating with incomplete observations, when no strong assumptions about the incompleteness mechanism are justified.Comment: Replaced with extended versio

Multi-Action Recognition via Stochastic Modelling of Optical Flow and Gradients

In this paper we propose a novel approach to multi-action recognition that performs joint segmentation and classification. This approach models each action using a Gaussian mixture using robust low-dimensional action features. Segmentation is achieved by performing classification on overlapping temporal windows, which are then merged to produce the final result. This approach is considerably less complicated than previous methods which use dynamic programming or computationally expensive hidden Markov models (HMMs). Initial experiments on a stitched version of the KTH dataset show that the proposed approach achieves an accuracy of 78.3%, outperforming a recent HMM-based approach which obtained 71.2%