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PubMed2002

No time loophole in Bell's theorem: the Hess-Philipp model is nonlocal.

Hess and Philipp recently claimed [(2001) Proc. Natl. Acad. Sci. USA 98, 14224-14227 and 14228-14233] that proofs of Bell's theorem have overlooked the possibility of time dependence in local hidden variables, hence the theorem has not been proven true. Moreover they present what is claimed to be a local realistic model of the EPR correlations. If this is true then Bell's theorem is not just unproven, but false. We refute both claims. First, we explain why time is not an issue in Bell's theorem, and second, we show that their hidden variables model violates Einstein separability. Hess and Philipp have overlooked the freedom of the experimenter to choose settings of a measurement apparatus at will: any setting could be in force during the same time period.

Journal Article↗

PubMed2004

Fitness-dependent topological properties of the world trade web.

Among the proposed network models, the hidden variable (or good get richer) one is particularly interesting, even if an explicit empirical test of its hypotheses has not yet been performed on a real network. Here we provide the first empirical test of this mechanism on the world trade web, the network defined by the trade relationships between world countries. We find that the power-law distributed gross domestic product can be successfully identified with the hidden variable (or fitness) determining the topology of the world trade web: all previously studied properties up to third-order correlation structure (degree distribution, degree correlations, and hierarchy) are found to be in excellent agreement with the predictions of the model. The choice of the connection probability is such that all realizations of the network with the same degree sequence are equiprobable.

Journal Article↗

PubMed2005

Wave model for conservative bound systems.

In the hidden variable theory, Bohm proved a connection between the Schrodinger and Hamilton-Jacobi equations and showed the existence of classical paths, for which the generalized Bohr quantization condition is valid. In this paper we prove similar properties, starting from the equivalence between the Schrodinger and wave equations in the case of the conservative bound systems. Our approach is based on the equations and postulates of quantum mechanics without using any additional postulate. Like in the hidden variable theory, the above properties are proven without using the approximation of geometrical optics or the semiclassical approximation. Since the classical paths have only a mathematical significance in our analysis, our approach is consistent with the postulates of quantum mechanics.

Journal Article↗

PubMed2006

GenRate: a generative model that reveals novel transcripts in genome-tiling microarray data.

Genome-wide microarray designs containing millions to hundreds of millions of probes are available for a variety of mammals, including mouse and human. These genome tiling arrays can potentially lead to significant advances in science and medicine, e.g., by indicating new genes and alternative primary and secondary transcripts. While bottom-up pattern matching techniques (e.g., hierarchical clustering) can be used to find gene structures in microarray data, we believe the many interacting hidden variables and complex noise patterns more naturally lead to an analysis based on generative models. We describe a generative model of tiling data and show how the sum-product algorithm can be used to infer hybridization noise, probe sensitivity, new transcripts, and alternative transcripts. The method, called GenRate, maximizes a global scoring function that enables multiple transcripts to compete for ownership of putative probes. We apply GenRate to a new exon tiling dataset from mouse chromosome 4 and show that it makes significantly more predictions than a previously described hierarchical clustering method at the same false positive rate. GenRate correctly predicts many known genes and also predicts new gene structures. As new problems arise, additional hidden variables can be incorporated into the model in a principled fashion, so we believe that GenRate will prove to be a useful tool in the new era of genome-wide tiling microarray analysis.

Animals↗

PubMed2003

Violation of a Bell-like inequality in single-neutron interferometry.

Non-local correlations between spatially separated systems have been extensively discussed in the context of the Einstein, Podolsky and Rosen (EPR) paradox and Bell's inequalities. Many proposals and experiments designed to test hidden variable theories and the violation of Bell's inequalities have been reported; usually, these involve correlated photons, although recently an experiment was performed with (9)Be(+) ions. Nevertheless, it is of considerable interest to show that such correlations (arising from quantum mechanical entanglement) are not simply a peculiarity of photons. Here we measure correlations between two degrees of freedom (comprising spatial and spin components) of single neutrons; this removes the need for a source of entangled neutron pairs, which would present a considerable technical challenge. A Bell-like inequality is introduced to clarify the correlations that can arise between observables of otherwise independent degrees of freedom. We demonstrate the violation of this Bell-like inequality: our measured value is 2.051 +/- 0.019, clearly above the value of 2 predicted by classical hidden variable theories.

Journal Article↗

PubMedDate not supplied

Qualitative theory of compartmental systems with lags.

Dynamic models of many processes in the biological and physical sciences give systems of ordinary differential equations called compartmental systems. Often, these systems include time lags; in this context, continuous probability density functions (pdfs) of lags are far more important than discrete lags. There is a relatively complete theory of compartmental systems without lags, both linear and non-linear [SIAM Rev. 35 (1993) 43]. The authors extend their previous work on compartmental systems without lags to show that, for discrete lags and for a very large class of pdfs of continuous lags, compartmental systems with lags are equivalent to larger compartmental systems without lags. Consequently, the properties of compartmental systems with lags are the same as those of compartmental systems without lags. For a very large class of compartmental systems with time lags, one can show that the time lags themselves can be generated by compartmental systems without lags. Thus, such systems can be partitioned into a main system, which is the original system without the lags, plus compartmental subsystems without lags that generate the lags. The latter may be linear or non-linear and may be inserted into main systems that are linear or non-linear. The state variables of the compartmental lag subsystems are hidden variables in the formulation with explicit lags.

Body Fluid Compartments↗

PubMed2006

Varying complexity in tree-structured image distribution models.

Probabilistic models of image statistics underlie many approaches in image analysis and processing. An important class of such models have variables whose dependency graph is a tree. If the hidden variables take values on a finite set, most computations with the model can be performed exactly, including the likelihood calculation, training with the EM algorithm, etc. Crouse et al. developed one such model, the hidden Markov tree (HMT). They took particular care to limit the complexity of their model. We argue that it is beneficial to allow more complex tree-structured models, describe the use of information theoretic penalties to choose the model complexity, and present experimental results to support these proposals. For these experiments, we use what we call the hierarchical image probability (HIP) model. The differences between the HIP and the HMT models include the use of multivariate Gaussians to model the distributions of local vectors of wavelet coefficients and the use of different numbers of hidden states at each resolution. We demonstrate the broad utility of image distributions by applying the HIP model to classification, synthesis, and compression, across a variety of image types, namely, electrooptical, synthetic aperture radar, and mammograms (digitized X-rays). In all cases, we compare with the HMT.

Algorithms↗

PubMed2006

Semi-supervised discovery of differential genes.

BACKGROUND: Various statistical scores have been proposed for evaluating the significance of genes that may exhibit differential expression between two or more controlled conditions. However, in many clinical studies to detect clinical marker genes for example, the conditions have not necessarily been controlled well, thus condition labels are sometimes hard to obtain due to physical, financial, and time costs. In such a situation, we can consider an unsupervised case where labels are not available or a semi-supervised case where labels are available for a part of the whole sample set, rather than a well-studied supervised case where all samples have their labels. RESULTS: We assume a latent variable model for the expression of active genes and apply the optimal discovery procedure (ODP) proposed by Storey (2005) to the model. Our latent variable model allows gene significance scores to be applied to unsupervised and semi-supervised cases. The ODP framework improves detectability by sharing the estimated parameters of null and alternative models of multiple tests over multiple genes. A theoretical consideration leads to two different interpretations of the latent variable, i.e., it only implicitly affects the alternative model through the model parameters, or it is explicitly included in the alternative model, so that the interpretations correspond to two different implementations of ODP. By comparing the two implementations through experiments with simulation data, we have found that sharing the latent variable estimation is effective for increasing the detectability of truly active genes. We also show that the unsupervised and semi-supervised rating of genes, which takes into account the samples without condition labels, can improve detection of active genes in real gene discovery problems. CONCLUSION: The experimental results indicate that the ODP framework is effective for hypotheses including latent variables and is further improved by sharing the estimations of hidden variables over multiple tests.

Algorithms↗

PubMed2002

An expectation maximization algorithm for training hidden substitution models.

We derive an expectation maximization algorithm for maximum-likelihood training of substitution rate matrices from multiple sequence alignments. The algorithm can be used to train hidden substitution models, where the structural context of a residue is treated as a hidden variable that can evolve over time. We used the algorithm to train hidden substitution matrices on protein alignments in the Pfam database. Measuring the accuracy of multiple alignment algorithms with reference to BAliBASE (a database of structural reference alignments) our substitution matrices consistently outperform the PAM series, with the improvement steadily increasing as up to four hidden site classes are added. We discuss several applications of this algorithm in bioinformatics.

Algorithms↗

PubMed2002

Linear modes of gene expression determined by independent component analysis.

MOTIVATION: The expression of genes is controlled by specific combinations of cellular variables. We applied Independent Component Analysis (ICA) to gene expression data, deriving a linear model based on hidden variables, which we term 'expression modes'. The expression of each gene is a linear function of the expression modes, where, according to the ICA model, the linear influences of different modes show a minimal statistical dependence, and their distributions deviate sharply from the normal distribution. RESULTS: Studying cell cycle-related gene expression in yeast, we found that the dominant expression modes could be related to distinct biological functions, such as phases of the cell cycle or the mating response. Analysis of human lymphocytes revealed modes that were related to characteristic differences between cell types. With both data sets, the linear influences of the dominant modes showed distributions with large tails, indicating the existence of specifically up- and downregulated target genes. The expression modes and their influences can be used to visualize the samples and genes in low-dimensional spaces. A projection to expression modes helps to highlight particular biological functions, to reduce noise, and to compress the data in a biologically sensible way.

Algorithms↗

PubMed2006

An hourly variation in zoo visitor interest: measurement and significance for animal welfare research.

A methodological difficulty facing welfare research on nonhuman animals in the zoo is the large number of uncontrolled variables due to variation within and between study sites. Zoo visitors act as uncontrolled variables, with number, density, size, and behavior constantly changing. This is worrisome because previous research linked visitor variables to animal behavioral changes indicative of stress. There are implications for research design: Studies not accounting for visitors' effect on animal welfare risk confounding (visitor) variables distorting their findings. Zoos need methods to measure and minimize effects of visitor behavior and to ensure that there are no hidden variables in research models. This article identifies a previously unreported variable--hourly variation (decrease) in visitor interest--that may impinge on animal welfare and validates a methodology for measuring it. That visitor interest wanes across the course of the day has important implications for animal welfare management; visitor effects on animal welfare are likely to occur, or intensify, during the morning or in earlier visits when visitor interest is greatest. This article discusses this issue and possible solutions to reduce visitor effects on animal well-being.

Animal Husbandry↗

PubMed1997

Psychiatric morbidity in primary public health care: a multicentre investigation. Part II. Hidden morbidity and choice of treatment.

A total of 1,281 patients were examined during consultation with their GP in a Nordic multicentre study focusing on the prevalence of psychiatric illness, hidden psychiatric morbidity, treatment and pathways to specialized care. The methodology and prevalence were reported in an accompanying paper. The present paper presents results concerning the variables hidden psychiatric morbidity, treatment and pathways to specialized care. The GPs detected 44% of the psychiatric cases compared with the result of a diagnostic interview (PSE). The distinction between psychosis and non-psychosis did not influence the GPs' ability to detect a mental illness. According to the GPs' assessment the majority of patients suffering from a mental disorder consulted their GP about physical complaints. The GPs treated the patients themselves, and only a limited number of cases were referred to psychiatrists or psychologists.

Adolescent↗

PubMed2004

SINBAD: a neocortical mechanism for discovering environmental variables and regularities hidden in sensory input.

We propose that a top priority of the cerebral cortex must be the discovery and explicit representation of the environmental variables that contribute as major factors to environmental regularities. Any neural representation in which such variables are represented only implicitly (thus requiring extra computing to use them) will make the regularities more complex and therefore more difficult, if not impossible, to learn. The task of discovering such important environmental variables is not an easy one since their existence is only indirectly suggested by the sensory input patterns the cortex receives--these variables are "hidden". We present a candidate computational strategy for (i) discovering regularity-simplifying environmental variables, (ii) learning the regularities, and (iii) using regularities in perceptual and decision-making tasks. The SINBAD computational model discovers useful environmental variables through a search for different, but nevertheless highly correlated, functions of any kind over nonoverlapping subsets of the known variables, this being indicative of some important environmental variable that is responsible for the correlation. We suggest that such a search is performed in the neocortex by the dendritic trees of individual pyramidal cells. According to the SINBAD model, the basic function of each pyramidal cell is to (i) discover and represent one of the regularity-simplifying environmental variables and (ii) learn to infer the state of its variable from the states of other variables, represented by other pyramidal cells. A network of such cells--each cell just attending to representation of its variable--can function as a sophisticated and useful inferential model of the outside world.

Association Learning↗

PubMed2003

A multi-scale probabilistic network model for detection, synthesis and compression in mammographic image analysis.

We develop a probabilistic network model over image spaces and demonstrate its broad utility in mammographic image analysis, particularly with respect to computer-aided diagnosis. The model employs a multi-scale pyramid decomposition to factor images across scale and a network of tree-structured hidden variables to capture long-range spatial dependencies. This factoring makes the computation of the density functions local and tractable. The result is a hierarchical mixture of conditional probabilities, similar to a hidden Markov model on a tree. The model parameters are found with maximum likelihood estimation using the expectation-maximization algorithm. The utility of the model is demonstrated for three applications: (1) detection of mammographic masses for computer-aided diagnosis; (2) qualitative assessment of model structure through mammographic synthesis; and (3) compression of mammographic regions of interest.

Female↗

PubMed2005

On the relationship between deterministic and probabilistic directed Graphical models: from Bayesian networks to recursive neural networks.

Machine learning methods that can handle variable-size structured data such as sequences and graphs include Bayesian networks (BNs) and Recursive Neural Networks (RNNs). In both classes of models, the data is modeled using a set of observed and hidden variables associated with the nodes of a directed acyclic graph. In BNs, the conditional relationships between parent and child variables are probabilistic, whereas in RNNs they are deterministic and parameterized by neural networks. Here, we study the formal relationship between both classes of models and show that when the source nodes variables are observed, RNNs can be viewed as limits, both in distribution and probability, of BNs with local conditional distributions that have vanishing covariance matrices and converge to delta functions. Conditions for uniform convergence are also given together with an analysis of the behavior and exactness of Belief Propagation (BP) in 'deterministic' BNs. Implications for the design of mixed architectures and the corresponding inference algorithms are briefly discussed.

Bayes Theorem↗

PubMed2006

Strengthening the case for disease management effectiveness: un-hiding the hidden bias.

As is the case with most health care program evaluations, disease management (DM) programs typically follow an observational study design, indicating that randomization to treatment or control was not performed. The foremost limitation of observational studies, compared to randomized studies, is that the only biases that can be controlled for are those associated with observed variables. Hidden bias refers to all those unobserved covariates that may distort the conclusions of the study. This paper introduces a sensitivity analysis that is used to determine the magnitude of hidden bias necessary to alter the conclusion that a DM program intervention was indeed effective.

Bias↗

PubMed1994

Combat-related posttraumatic stress disorder symptoms in older men.

Nearly 25% of U.S. men aged 55 or older served in combat, yet its impact on aging is unknown. The relationship of posttraumatic stress disorder (PTSD) symptoms to combat exposure was examined in 1,210 veterans of World War II (WWII) and the Korean War, who were participants in the Normative Aging Study. Over 54% of WWII and 19% of Korean veterans reported combat experience. The relationship between combat exposure and PTSD symptoms was stronger in the WWII cohort. The sample prevalence of PTSD by combat exposure ranged from 0% to 12.4%, differing by the PTSD measure. WWII veterans exposed to moderate or heavy combat had 13.3 times greater risk of PTSD symptoms measured 45 years later, compared with noncombat veterans. It is suggested that military service in general, and combat exposure in particular, is a "hidden variable" in the study of aging men.

Adult↗

PubMed2003

An approximate maximum likelihood approach, applied to phylogenetic trees.

A novel type of approximation scheme to the maximum likelihood (ML) approach is presented and discussed in the context of phylogenetic tree reconstruction from aligned DNA sequences. It is based on a parameterized approximation to the conditional distribution of hidden variables (related, e.g., to the sequences of unobserved branch point ancestors) given the observed data. A modified likelihood, based on the extended data, is then maximized with respect to the parameters of the model as well as to those involved in the approximation. With a suitable form of the approximation, the proposed method allows for simpler updating of the parameters, at the cost of an increased parameter count and a slight decrease in performance. The method is tested on phylogenetic tree reconstruction from artificially generated sequences, and its performance is compared to that of ML, showing that the approach is competitive for reasonably similar sequences. The method is also applied to real DNA sequences from primates, yielding a result consistent with those obtained by other standard algorithms.

Animals↗