Conditional Independence

The main task in this essay entails modeling a finite sequence of forward Euribor interest rates as continuous-time stochastic processes under several equivalent martingale probability measures, and in particular, under the terminal measure. To achieve this, we consider a continuous trading economy that is free from arbitrage, and further proceed to implement a Monte Carlo method for pricing interest rate derivatives such as caps and caplets within these forward Euribor rate processes. We briefly review tools for stochastic differential equations and use this knowledge to construct the equation describing the dynamics of the Euribor market model, wherein prices of trading assets become martingales.

The main task in this essay entails modeling a finite sequence of forward Euribor interest rates as continuous-time stochastic processes under several equivalent martingale probability measures, and in particular, under the terminal measure. To achieve this, we consider a continuous trading economy that is free from arbitrage, and further proceed to implement a Monte Carlo method for pricing interest rate derivatives such as caps and caplets within these forward Euribor rate processes. We briefly review tools for stochastic differential equations and use this knowledge to construct the equation describing the dynamics of the Euribor market model, wherein prices of trading assets become martingales.

Most previous information retrieval (IR) models assume that terms of queries and documents are statistically independent from each another. However, independence assumption is obviously and openly understood to be wrong, so we present a new method of incorporating term dependence in probabilistic retrieval model by adapting a structural index system using dependency parse tree and the Chow Expansion to compensate the weakness of the assumption. In this paper, we describe a theoretic process to apply the Chow Expansion to the general probabilistic models and the state-of-the-art 2-Poisson model, and we re-examine the weight of phrase terms. Through the experiments on document collections, ETRI-KEMONG in Korean, we demonstrate that the incorporation of term dependences using the Chow Expansion contribute to the improvement of performance in Probabilistic IR systems.

Studying the neuronal pattern of interactions may help us to understand the underlying processes of functional connectivity in the brain. Simultaneous recording of multiple neuronal activities using a multi electrode array provides rich neuronal signals and requires appropriate statistical and computational methods to demonstrate any connectivity. Using ordinary coherence to infer true connectivity between two neurons is subject to influence from other intermediate neurons (predictors). This study uses multivariate partial coherence analysis to estimate the synchronization of spiking neurons from recorded signals. The objective is to develop an algorithm to differentiate between conditional and unconditional independence among neurons. This may provide useful information on how neurons interact to transmit or receive signals by taking into account the influence from the predictors. In this paper, we validate the method of multivariate partial coherence analysis on a network of spiking neurons consisting of nine interconnected neurons simulated by the Izhikevich model. Then we implement this method on physiological signals to infer the connectivity among ten neurons recorded across different areas of rat hippocampus. Our analyses show the applicability of the proposed method for identifying the true connectivity in the simulated data. We also present the effect of predictor neurons on pairwise indirect relationships within specific frequency content. Conditional independence links in real data are reduced by 53% compared with unconditional links. The proposed method could be a valuable tool for observing the connectivity between neurons during normal and abnormal cognitive responses.

Background. The ability to infer network structure from multivariate neuronal signals is central to computational neuroscience. Directed network analyses typically use parametric approaches based on auto-regressive (AR) models, where networks are constructed from estimates of AR model parameters. However, the validity of using low order AR models for neurophysiological signals has been questioned. A recent article introduced a non parametric approach to estimate directionality in bivariate data, non parametric approaches are free from concerns over model validity. New Method. We extend the non parametric framework to include measures of directed conditional independence, using scalar measures that decompose the overall partial correlation coefficient summatively by direction, and a set of functions that decompose the partial coherence summatively by direction. A time domain partial correlation function allows both time and frequency views of the data to be constructed. The conditional independence estimates are conditioned on a single predictor. Results. The framework is applied to simulated cortical neuron networks and mixtures of Gaussian time series data with known interactions. It is applied to experimental data consisting of local field potential recordings from bilateral hippocampus in anaesthetised rats. Comparison with Existing Method(s). The framework offers a non parametric approach to estimation of directed interactions in multivariate neuronal recordings, and increased flexibility in dealing with both spike train and time series data. Conclusions. The framework offers a novel alternative non parametric approach to estimate directed interactions in multivariate neuronal recordings, and is applicable to spike train and time series data

Summary Graphical models oer simple and intuitive interpretations in terms of conditional independence relationships, and these are especially valuable when large numbers of variables are involved. In some settings restrictions upon experiments, number of variables, and other forms of data collection may result in our being able to estimate only parts of a large graphical model. Consider a collectionC of submodels of a decomposable graphG. In this article, we address the problem of combining component graphical models, and a theory is derived to the eect that one can combine the collection C of decomposable graphs,G1;G2; ;Gm, into a larger decomposable graph, H, of the variables that are involved in G so that the conditional independence relationships inG1;G2; ;Gm may be preserved inH. It is also shown that theH which contains the actual graphG as a subgraph is determined uniquely.

We propose an algorithm for combining decomposable graphical models and apply it for building decomposable graphical log-linear models which involve a large number of variables. A main idea in this algorithm is that we group the random variables that are involved in the data into several subsets of variables, build graphical log-linear models for the marginal data, and then combine the marginal models using graphs of prime separators (section 2). The application of the algorithm to a data set of 40 binary variables is very successful, yielding a model which is mostly the same as the true one.

Let (X, Z) be a continuous random vector in R × R d , d ≥ 1. In this paper, we define the notion of a nonparametric residual of X on Z that is always independent of the predictor Z. We study its properties and show that the proposed notion of residual matches with the usual residual (error) in a multivariate normal regression model. Given a random vector (X, Y, Z) in R × R × R d , we use this notion of residual to show that the conditional independence between X and Y , given Z, is equivalent to the mutual independence of the residuals (of X on Z and Y on Z) and Z. This result is used to develop a test for conditional independence. We propose a bootstrap scheme to approximate the critical value of this test. We compare the proposed test, which is easily implementable, with some of the existing procedures through a simulation study.

Let (X, Z) be a continuous random vector in R × R d , d ≥ 1. In this paper, we define the notion of a nonparametric residual of X on Z that is always independent of the predictor Z. We study its properties and show that the proposed notion of residual matches with the usual residual (error) in a multivariate normal regression model. Given a random vector (X, Y, Z) in R × R × R d , we use this notion of residual to show that the conditional independence between X and Y , given Z, is equivalent to the mutual independence of the residuals (of X on Z and Y on Z) and Z. This result is used to develop a test for conditional independence. We propose a bootstrap scheme to approximate the critical value of this test. We compare the proposed test, which is easily implementable, with some of the existing procedures through a simulation study.

Mastering the dynamics of social influence requires separating, in a database of information propagation traces, the genuine causal processes from temporal correlation, i.e., homophily and other spurious causes. However, most studies to characterize social influence, and, in general, most data-science analyses focus on correlations, statistical independence, or conditional independence. Only recently, there has been a resurgence of interest in "causal data science, " e.g., grounded on causality theories. In this paper we adopt a principled causal approach to the analysis of social influence from informationpropagation data, rooted in the theory of probabilistic causation. Our approach consists of two phases. In the first one, in order to avoid the pitfalls of misinterpreting causation when the data spans a mixture of several subtypes ("Simpson's paradox"), we partition the set of propagation traces into groups, in such a way that each group is as less contradictory as possible in terms of the hierarchical structure of information propagation. To achieve this goal, we borrow the notion of "agony" and define the Agony-bounded Partitioning problem, which we prove being hard, and for which we develop two efficient algorithms with approximation guarantees. In the second phase, for each group from the first phase, we apply a constrained MLE approach to ultimately learn a minimal causal topology. Experiments on synthetic data show that our method is able to retrieve the genuine causal arcs w.r.t. a ground-truth generative model. Experiments on real data show that, by focusing only on the extracted causal structures instead of the whole social graph, the effectiveness of predicting influence spread is significantly improved.

In this paper, we give a construction of wavelets which are (a) semiorthogonal with respect to an arbitrary elliptic bilinear form a(., .) on the Sobolev space HO((0. L ) ) and (b) continuous and piecewise linear on an arbitrary partition of [O? L]. We illustrate this construction using the model problem 2 I 1 -€ U

This paper shows the description of our team Borregos from the Tecnologico de Monterrey, Campus Monterrey. Borregos team has been participating in the RoboCup competitions since 2004, starting in the 2D Simulation League and moving forward to the 3D Simulation League with spheres in 2006, the 3D Simulation League with humanoids in 2007 and the RoboStadium Simulation League since 2008. In 2009 we started a new team “Borregos Humanoids” which participated in the Mexican RoboCup Open. In 2010 we also qualified in the Standard Platform League and 3D Simulation League in the RoboCup Singapore 2010 competitions. In 2010 and 2011 we won the 2nd place in the Robotstadium competition. In 2011 we rebuild the 2D Simulation League team and started a new code base for the team in the Java Platform.

One of the largest determinants of client outcomes is the counselor who provides treatment. Therapists often vary widely in effectiveness, even when delivering standardized manual-guided treatment. In particular, the therapeutic skill of accurate empathy originally described by Carl Rogers has been found to account for a meaningful proportion of variance in therapeutic alliance and in addiction treatment outcomes. High-empathy counselors appear to have higher success rates regardless of theoretical orientation. Low-empathy and confrontational counseling, in contrast, has been associated with higher drop-out and relapse rates, weaker therapeutic alliance and less client change. The authors propose emphasis on empathic listening skills as an evidencebased practice in the hiring and training of counselors to improve outcomes and prevent harm in addiction treatment.

We estimate the effect of early child development on maternal labor force participation using data from teacher assessments. Mothers might react to having a poorly developing child by dropping out of the formal labor force in order to spend more time with their child, or they could potentially increase their labor supply to be able to provide the funds for better education and health resources. Which action dominates is therefore the empirical question we seek to answer in this paper. Importantly, we control for the potential endogeneity of child development by using an instrumental variables approach, uniquely exploiting exogenous variation in child development associated with child handedness. We find that having a poorly developing young child reduces the probability that a mother will participate in the labor market by about 25 percentage points.

Descriptive, principal component (PCA), and thin-plate spline (TPS) analyses of theropod third metatarsals (MT III) definitively segregate the arctometatarsus from other theropod pedal morphologies and reveal variation within phylogenetic and functional subgroups of metatarsi. PCA indicates that the arctometatarsalian MT III differs in shape from the nonarctometatarsalian condition independently of size, indicating that allometric differences among taxa produced this divergence in MT III shape. TPS indicates substantial transfer of footfall force from MT II to MT III in ornithomimids and tyrannosaurids and from MT IV to MT III in troodontids. The study suggests different modes of ligament-damped sagittal rotation of MT III in tyrannosaurids, ornithomimids, and troodontids. Deinonychus had a large MT II-MT III articulation consistent with resisting forces of predatory strikes, while MT III of some large carnosaurs are less robust than expected. Phylogenetic bracketing suggests that proximal intermetatarsal ligaments in theropods were a key innovation preceding arctometatarsus evolution. A Bayesian phylogenetic analysis indicates that an arctometatarsus evolved in the common ancestor of the Tyrannosauridae + (Ornithomimosauria + Troodontidae) clade, but other optimizations are plausible. The most likely selective benefit of the structure was increased agility; if so, homoplasy indicates multiple exaptive and adaptive pathways towards predation and escape roles.

Feature selection is a key task in statistical pattern recognition. Most feature selection algorithms have been proposed based on specific objective functions which are usually intuitively reasonable but can sometimes be far from the more basic objectives of the feature selection. This paper describes how to select features such that the basic objectives, e.g., classification or clustering accuracies, can be optimized in a more direct way. The analysis requires that the contribution of each feature to the evaluation metrics can be quantitatively described by some score function. Motivated by the conditional independence structure in probabilistic distributions, the analysis uses a leave-one-out feature selection algorithm which provides an approximate solution. The leave-oneout algorithm improves the conventional greedy backward elimination algorithm by preserving more interactions among features in the selection process, so that the various feature selection objectives can be optimized in a unified way. Experiments on six real-world datasets with different feature evaluation metrics have shown that this algorithm outperforms popular feature selection algorithms in most situations.

Feature selection is a key task in statistical pattern recognition. Most feature selection algorithms have been proposed based on specific objective functions which are usually intuitively reasonable but can sometimes be far from the more basic objectives of the feature selection. This paper describes how to select features such that the basic objectives, e.g., classification or clustering accuracies, can be optimized in a more direct way. The analysis requires that the contribution of each feature to the evaluation metrics can be quantitatively described by some score function. Motivated by the conditional independence structure in probabilistic distributions, the analysis uses a leave-one-out feature selection algorithm which provides an approximate solution. The leave-oneout algorithm improves the conventional greedy backward elimination algorithm by preserving more interactions among features in the selection process, so that the various feature selection objectives can be optimized in a unified way. Experiments on six real-world datasets with different feature evaluation metrics have shown that this algorithm outperforms popular feature selection algorithms in most situations.

Belief space planning (BSP) is a fundamental problem in robotics. Determining an optimal action quickly grows intractable as it involves calculating the expected accumulated cost (reward), where the expectation accounts for all future measurement realizations. State of the art approaches therefore resort to simplifying assumptions and approximations to reduce computational complexity. Importantly, while in robotics re-planning is essential, these approaches calculate each planning session from scratch. In this work we contribute a novel approach, iX-BSP, that is based on the key insight that calculations in consecutive planning sessions are similar in nature and can be thus re-used. Our approach performs incremental calculation of the expectation by appropriately re-using computations already performed in a precursory planing session while accounting for the information obtained in inference between the two planning sessions. The formulation of our approach considers general distrib...

A new graphical model, called a vine, for dependent random variables is introduced. Vines generalize the Markov trees often used in modelling highdimensional distributions. They differ from Markov trees and Bayesian belief nets in that the concept of conditional independence is weakened to allow for various forms of conditional dependence. Vines can be used to specify multivariate distributions in a straightforward way by specifying various marginal distributions and the ways in which these marginals are to be coupled. Such distributions have applications in uncertainty analysis where the objective is to determine the sensitivity of a model output with respect to the uncertainty in unknown parameters. Expert information is frequently elicited to determine some quantitative characteristics of the distribution such as (rank) correlations. We show that it is simple to construct a minimum information vine distribution, given such expert information. Sampling from minimum information distributions with given marginals and (conditional) rank correlations specified on a vine can be performed almost as fast as independent sampling. A special case of the vine construction generalizes work of Joe and allows the construction of a multivariate normal distribution by specifying a set of partial correlations on which there are no restrictions except the obvious one that a correlation lies between -1 and 1.

Chromosome 1q has been implicated in the etiology of schizophrenia in several independent studies. However, the peak linkage findings have been dispersed over a large chromosomal region, with negative findings in this region also being reported. Our group has previously observed linkage on chromosome 1q42, maximizing within the DISC1 gene, which has also been implied in the etiology of schizophrenia based on functional studies. In the study presented here, we genotyped 300 polymorphic markers on chromosome 1 using a study sample of 70 families with multiple individuals affected with schizophrenia or related conditions, independent of the study samples in our previous reports. We again found evidence for linkage on 1q42 maximizing within the DISC1 gene (rs1000731, lod ¼ 2.70). Further, a haplotype containing the most strongly linked markers showed some evidence of association with the disease. This replicates the previous linkage finding in the same region and constitutes supportive evidence for a susceptibility gene in this region.

This paper presents a novel repeated latent class model for a longitudinal response that is frequently measured as in our prospective study of older adults with monthly data on activities of daily living (ADL) for more than ten years. The proposed method is especially useful when the longitudinal response is measured much more frequently than other relevant covariates. The repeated trajectory classes represent distinct temporal patterns of the longitudinal response wherein an individual's membership in the trajectory classes may renew or change over time. Within a trajectory class, the longitudinal response is modeled by a class-specific generalized linear mixed model. Effectively, an individual may remain in a trajectory class or switch to another as the class membership predictors are updated periodically over time. The identification of a common set of trajectory classes allows changes among the temporal patterns to be distinguished from local fluctuations in the response. An informative event such as death is jointly modeled by class-specific probability of the event through shared random effects. We do not impose the conditional independence assumption given the classes. The method is illustrated by analyzing the change over time in ADL trajectory class among 754 older adults with 70500 person-months of follow-up in the Precipitating Events Project. We also investigate the impact of jointly modeling the class-specific probability of the event on the parameter estimates in a simulation study. The primary contribution of our paper is the periodic updating of trajectory classes for a longitudinal categorical response without assuming conditional independence.

We present and demonstrate a particle filtering approach to data fusion and situation assessment for military operations in urban environments. Our approach views such an environment as a physical system whose state vector is composed of a large number of both discrete and continuous variables representing properties of tracked entities. Inference on such vector-based models exploits both causal dependencies among variables in the state vector via its dynamic Bayesian belief network representation and vector decomposition into weakly interacting subcomponents. To effectively leverage the decomposition, instead of straightforward particle filtering, the proposed algorithm maintains factored particles over clusters of state variables, thus resulting in smaller variance. The algorithm samples discrete modes and approximates the continuous variables by a multi-normal distribution updated at each time step by an unscented Kalman filter. The approach is demonstrated using a Marine Corps operational scenario involving a potential ambush on city streets.