Bayesian Search Research Articles

Parallel Bayesian Search with No Coordination

Coordinating the actions of agents (e.g., volunteers analyzing radio signals in SETI@home) yields efficient search algorithms. However, such an efficiency is often at the cost of implementing complex coordination mechanisms which may be expensive in terms of communication and/or computation overheads. Instead, non-coordinating algorithms, in which each agent operates independently from the others, are typically very simple, and easy to implement. They are also inherently robust to slight misbehaviors, or even crashes of agents. In this article, we investigate the “price of non-coordinating,” in terms of search performance, and we show that this price is actually quite small. Specifically, we consider a parallel version of a classical Bayesian search problem, where set of k ≥1 searchers are looking for a treasure placed in one of the boxes indexed by positive integers, according to some distribution p . Each searcher can open a random box at each step, and the objective is to find the treasure in a minimum number of steps. We show that there is a very simple non-coordinating algorithm which has expected running time at most 4(1−1/ k +1) 2 OPT+10, where OPT is the expected running time of the best fully coordinated algorithm. Our algorithm does not even use the precise description of the distribution p , but only the relative likelihood of the boxes. We prove that, under this restriction, our algorithm has the best possible competitive ratio with respect to OPT. For the case where a complete description of the distribution p is given to the search algorithm, we describe an optimal non-coordinating algorithm for Bayesian search. This latter algorithm can be twice as fast as our former algorithm in practical scenarios such as uniform distributions. All these results provide a complete characterization of non-coordinating Bayesian search. The take-away message is that, for their simplicity and robustness, non-coordinating algorithms are viable alternatives to complex coordinating mechanisms subject to significant overheads. Most of these results apply as well to linear search, in which the indices of the boxes reflect their relative importance, and where important boxes must be visited first.

Resolution invariant wavelet features of melanoma studied by SVM classifiers.

This article refers to the Computer Aided Diagnosis of the melanoma skin cancer. We derive wavelet-based features of melanoma from the dermoscopic images of pigmental skin lesions and apply binary C-SVM classifiers to discriminate malignant melanoma from dysplastic nevus. The aim of this research is to select the most efficient model of the SVM classifier for various image resolutions and to search for the best resolution-invariant wavelet bases. We show AUC as a function of the wavelet number and SVM kernels optimized by the Bayesian search for two independent data sets. Our results are compatible with the previous experiments to discriminate melanoma in dermoscopy images with ensembling and feed-forward neural networks.

Accurate and reliable estimation of kinetic parameters for environmental engineering applications: A global, multi objective, Bayesian optimization approach

Accurate and reliable predictions of bacterial growth and metabolism from unstructured kinetic models are critical to the proper operation and design of engineered biological treatment and remediation systems. As such, parameter estimation has progressed into a routine challenge in the field of Environmental Engineering. Among the main issues identified with parameter estimation, the model-data calibration approach is a crucial, yet an often overlooked and difficult optimization problem. Here, a novel and rigorous global, multi objective, and fully Bayesian optimization approach that overcomes challenges associated with multi-variate, sparse and noisy data, as well as highly non-linear model structures commonly encountered in Environmental Engineering practice is presented. This optimization approach allows an improved definition and targeting of the compromise solution space for all multivariate problems, allowing efficient convergence, and a Bayesian component to thoroughly explore parameter and model prediction uncertainty. This global optimization approach outperformed, in terms of parameter accuracy and precision, standard, local non-linear regression routines and overcomes issues associated with premature convergence and addresses overfitting of different variables in the calibration process.•A sequential single, multi-objective, and Bayesian optimization workflow was developed to accurately and reliably estimate unstructured kinetic model parameters.•The global, single objective approach defines the global optimum (the best compromise solution) and “extreme” parameter solutions for each variable, while the global, multi-objective approach confirms the “best” compromise solution space for the Bayesian search to target and convergence is assessed using the single objective results.•The Approximate Bayesian Computational approach fully explores parameter and model prediction uncertainty targeting the compromise solution space previously identified.

A Monte Carlo Study of Time Varying Coefficient (TVC) Estimation

A number of recent papers have proposed a time-varying-coefficient (TVC) procedure that, in theory, yields consistent parameter estimates in the presence of measurement errors, omitted variables, incorrect functional forms, and simultaneity. The key element of the procedure is the selection of a set of driver variables. With an ideal driver set the procedure is both consistent and efficient. However, in practice it is not possible to know if a perfect driver set exists. We construct a number of Monte Carlo experiments to examine the performance of the methodology under (i) clearly-defined conditions and (ii) a range of model misspecifications. We also propose a new Bayesian search technique for the set of driver variables underlying the TVC methodology. Experiments are performed to allow for incorrectly specified functional form, omitted variables, measurement errors, unknown nonlinearity and endogeneity. In all cases except the last, the technique works well in reasonably small samples.

The efficiency improvement of port state control based on ship accident Bayesian networks

Ship accident has always been the focus in shipping and it is concerned by port state authorities. This study tries to investigate the impact of various factors on ship accident along with the port state’s detected deficiency items. Very importantly, it manages to identify the structural connections between the checked deficiency items. The data used in this study are mainly from Lloyd’s register of shipping, International Maritime Organization and Tokyo Memorandum of Understanding, with a total of 64,847 observations obtained. The Bayesian network model is employed and the Greedy thick thinning and Bayesian search algorithms are used to learn the structural networks. In addition to the impacts of the deficiency items and the ship inherent attributes on ship accidents, this study identifies some key deficiency items for port states. It also analyzes the intense connections between the key deficiency items with others. This helps simplify the port state’s inspection procedure and improve operational efficiency.

Bayesian adaptive algorithms for locating HIV mobile testing services

BackgroundWe have previously conducted computer-based tournaments to compare the yield of alternative approaches to deploying mobile HIV testing services in settings where the prevalence of undetected infection may be characterized by ‘hotspots’. We report here on three refinements to our prior assessments and their implications for decision-making. Specifically, (1) enlarging the number of geographic zones; (2) including spatial correlation in the prevalence of undetected infection; and (3) evaluating a prospective search algorithm that accounts for such correlation.MethodsBuilding on our prior work, we used a simulation model to create a hypothetical city consisting of up to 100 contiguous geographic zones. Each zone was randomly assigned a prevalence of undetected HIV infection. We employed a user-defined weighting scheme to correlate infection levels between adjacent zones. Over 180 days, search algorithms selected a zone in which to conduct a fixed number of HIV tests. Algorithms were permitted to observe the results of their own prior testing activities and to use that information in choosing where to test in subsequent rounds. The algorithms were (1) Thompson sampling (TS), an adaptive Bayesian search strategy; (2) Besag York Mollié (BYM), a Bayesian hierarchical model; and (3) Clairvoyance, a benchmarking strategy with access to perfect information.ResultsOver 250 tournament runs, BYM detected 65.3% (compared to 55.1% for TS) of the cases identified by Clairvoyance. BYM outperformed TS in all sensitivity analyses, except when there was a small number of zones (i.e., 16 zones in a 4 × 4 grid), wherein there was no significant difference in the yield of the two strategies. Though settings of no, low, medium, and high spatial correlation in the data were examined, differences in these levels did not have a significant effect on the relative performance of BYM versus TS.ConclusionsBYM narrowly outperformed TS in our simulation, suggesting that small improvements in yield can be achieved by accounting for spatial correlation. However, the comparative simplicity with which TS can be implemented makes a field evaluation critical to understanding the practical value of either of these algorithms as an alternative to existing approaches for deploying HIV testing resources.

A frequency-calibrated Bayesian search for new particles

The statistical procedure used in the search for new particles is investigated in this paper. The discovery of the Higgs particles is used to lay out the problem and the existing procedures. A Bayesian hierarchical model is proposed to address inference about the parameters of interest while incorporating uncertainty about the nuisance parameters into the model. In addition to inference, a decision making procedure is proposed. A loss function is introduced that mimics the important features of a discovery problem. Given the importance of controlling the “false discovery” and “missed detection” error rates in discovering new phenomena, the proposed procedure is calibrated to control for these error rates.

Distress-dependent temporal variability of regions encoding domain-specific and domain-general behavioral manifestations of phantom percepts.

Tinnitus is the perception of a phantom sound characterized behaviorally by a loudness and a distress component. Although a wealth of information is available about the relationship between these behavioral correlates and changes in static functional connectivity, its relationship with dynamic changes in network connectivity is yet unexplored. The aim of this study was thus to investigate changes in the flexibility and stability of temporal variability in tinnitus and its relation to loudness and distress using continuous resting-state EEG. We observe an increase in temporal variability at the whole-brain level in tinnitus, which is spatiotemporally distributed at the nodal level. Behaviorally, we observe changes in the relationship between temporal variability and loudness and distress depending on the amount of distress experienced. In patients with low distress, there is no relationship between temporal variability and loudness or distress, demonstrating a resilience in dynamic connectivity of the brain. However, patients with high distress exhibit a direct relationship with increasing loudness in the primary auditory cortex and parahippocampus, and an inverse relationship with increasing distress in the parahippocampus. In tinnitus, the specific sensory (loudness) component related to increased temporal variability possibly reflects a Bayesian search for updating deafferentation-based missing information. On the other hand, the decreased temporal variability related to the nonspecific distress component possibly reflects a more hard-wired or less adaptive contextual processing. Therefore, our findings may reveal a way to understand the changes in network dynamics not just in tinnitus, but also in other brain disorders.

Bayesian variable selection and coefficient estimation in heteroscedastic linear regression model

ABSTRACTIn many real applications, such as econometrics, biological sciences, radio-immunoassay, finance, and medicine, the usual assumption of constant error variance may be unrealistic. Ignoring heteroscedasticity (non-constant error variance), if it is present in the data, may lead to incorrect inferences and inefficient estimation. In this paper, a simple and effcient Gibbs sampling algorithm is proposed, based on a heteroscedastic linear regression model with an penalty. Then, a Bayesian stochastic search variable selection method is proposed for subset selection. Simulations and real data examples are used to compare the performance of the proposed methods with other existing methods. The results indicate that the proposal performs well in the simulations and real data examples. R code is available upon request.

A Markov chain Monte Carlo algorithm for Bayesian policy search

ABSTRACTPolicy search algorithms have facilitated application of Reinforcement Learning (RL) to dynamic systems, such as control of robots. Many policy search algorithms are based on the policy gradient, and thus may suffer from slow convergence or local optima complications. In this paper, we take a Bayesian approach to policy search under RL paradigm, for the problem of controlling a discrete time Markov decision process with continuous state and action spaces and with a multiplicative reward structure. For this purpose, we assume a prior over policy parameters and aim for the ‘posterior’ distribution where the ‘likelihood’ is the expected reward. We propound a Markov chain Monte Carlo algorithm as a method of generating samples for policy parameters from this posterior. The proposed algorithm is compared with certain well-known policy gradient-based RL methods and exhibits more appropriate performance in terms of time response and convergence rate, when applied to a nonlinear model of a Cart-Pole benchmark.

An Adaptive Approach to Locating Mobile HIV Testing Services.

Public health agencies suggest targeting "hotspots" to identify individuals with undetected HIV infection. However, definitions of hotspots vary. Little is known about how best to target mobile HIV testing resources. We conducted a computer-based tournament to compare the yield of 4 algorithms for mobile HIV testing. Over 180 rounds of play, the algorithms selected 1 of 3 hypothetical zones, each with unknown prevalence of undiagnosed HIV, in which to conduct a fixed number of HIV tests. The algorithms were: 1) Thompson Sampling, an adaptive Bayesian search strategy; 2) Explore-then-Exploit, a strategy that initially draws comparable samples from all zones and then devotes all remaining rounds of play to HIV testing in whichever zone produced the highest observed yield; 3) Retrospection, a strategy using only base prevalence information; and; 4) Clairvoyance, a benchmarking strategy that employs perfect information about HIV prevalence in each zone. Over 250 tournament runs, Thompson Sampling outperformed Explore-then-Exploit 66% of the time, identifying 15% more cases. Thompson Sampling's superiority persisted in a variety of circumstances examined in the sensitivity analysis. Case detection rates using Thompson Sampling were, on average, within 90% of the benchmark established by Clairvoyance. Retrospection was consistently the poorest performer. We did not consider either selection bias (i.e., the correlation between infection status and the decision to obtain an HIV test) or the costs of relocation to another zone from one round of play to the next. Adaptive methods like Thompson Sampling for mobile HIV testing are practical and effective, and may have advantages over other commonly used strategies.

Modeling Causal Relationships among Brain Areas in the Mesocorticolimbic System during Resting-State in Cocaine Users Utilizing a Graph Theoretic Approach.

ObjectiveWhile effective connectivity (EC, causal interaction) between brain areas has been investigated in chronic users of cocaine as they view cocaine pictures cues, no study has examined EC while they take part in a resting-state scan. This resting-state fMRI study aims to investigate the causal interaction among brain areas in the mesocorticolimbic system (MCLS), which is involved in reward and motivation, in cocaine users (vs. controls).MethodTwenty cocaine users and 17 healthy controls finished a structural and a resting-state scan. Mean voxel-based time series data were obtained from brain regions of interest (ROIs) from the MCLS, and were input into a Bayesian search algorithm called IMaGES.ResultsThe causal interaction pattern was different between the two groups. The feed-forward pattern found in cocaine smokers, between 7 ROIs of the MCLS during resting-state [ventral tegmental area (VTA)→hippocampus (HIPP)→ventral striatum (VenStri)→orbital frontal cortex (OFC), medial frontal cortex (MFC), anterior cingulate cortex (ACC), dorsolateral prefrontal cortex (DLPFC)], was absent in controls. That is, the subcortical VenStri area had a causal influence on four cortical brain areas only in cocaine users.ConclusionsDuring the resting-state scan, the VTA of cocaine smokers abstinent for at least 72 hours, but not controls, begins causal connections to limbic, midbrain, and frontal regions in the MCLS in a feed-forward manner. Following replication, further studies may assess if changes over time in EC during resting-state predict cocaine treatment efficacy and outcome.

Planck2015 results

Maps of cosmic microwave background (CMB) temperature and polarization from the 2015 release of Planck data provide the highestquality full-sky view of the surface of last scattering available to date. This enables us to detect possible departures from a globally isotropic cosmology. We present the first searches using CMB polarization for correlations induced by a possible non-trivial topology with a fundamental domain that intersects, or nearly intersects, the last-scattering surface (at comoving distance χrec), both via a direct scan for matched circular patterns at the intersections and by an optimal likelihood calculation for specific topologies. We specialize to flat spaces with cubic toroidal (T3) and slab (T1) topologies, finding that explicit searches for the latter are sensitive to other topologies with antipodal symmetry. These searches yield no detection of a compact topology with a scale below the diameter of the last-scattering surface. The limits on the radius ℛi of the largest sphere inscribed in the fundamental domain (at log-likelihood ratio Δlnℒ > −5 relative to a simply-connected flat Planck best-fit model) are: ℛi > 0.97 χrec for the T3 cubic torus; and ℛi > 0.56 χrec for the T1 slab. The limit for the T3 cubic torus from the matched-circles search is numerically equivalent, ℛi > 0.97 χrec at 99% confidence level from polarization data alone. We also perform a Bayesian search for an anisotropic global Bianchi VIIh geometry. In the non-physical setting, where the Bianchi cosmology is decoupled from the standard cosmology, Planck temperature data favour the inclusion of a Bianchi component with a Bayes factor of at least 2.3 units of log-evidence. However, the cosmological parameters that generate this pattern are in strong disagreement with those found from CMB anisotropy data alone. Fitting the induced polarization pattern for this model to the Planck data requires an amplitude of −0.10 ± 0.04 compared to the value of + 1 if the model were to be correct. In the physically motivated setting, where the Bianchi parameters are coupled and fitted simultaneously with the standard cosmological parameters, we find no evidence for a Bianchi VIIh cosmology and constrain the vorticity of such models to (ω/H)0 < 7.6 × 10-10 (95% CL).

Modelo de inventario multi-producto, con pronósticos de demanda y optimización Bayesiana

La complejidad de las cadenas de suministro exige mejores métodos para programar los inventarios de una empresa. En este trabajo se presenta una comparación entre modelos de pronósticos de demanda de múltiples productos, eligiendo el mejor entre: ARIMA, Suavización exponencial, Regresión Lineal Bayesiana y un Modelo Lineal Dinámico Bayesiano. Para ello, primero se realiza una simulación de casos donde no hay una Distribución Normal en las series de tiempo, segundo, se estiman las predicciones de ventas de tres productos de una estación de servicios de gasolina con los cuatro modelos, encontrando los mejores resultados para la Regresión Lineal Bayesiana. Seguido a esto, se presenta la optimización de un Modelo de Inventarios Multi-Producto. Para definir la política de pedidos, inventarios, costos y ganancias, se utiliza una búsqueda bayesiana, que integra elementos de búsqueda Tabú para mejorar la solución. Dicha Optimización del Modelo de Inventarios se aplica a un caso de una estación de combustibles en Colombia.

BAYESIAN ANALYSIS OF COSMIC RAY PROPAGATION: EVIDENCE AGAINST HOMOGENEOUS DIFFUSION.

We present the results of the most complete scan of the parameter space for cosmic ray (CR) injection and propagation. We perform a Bayesian search of the main GALPROP parameters, using the MultiNest nested sampling algorithm, augmented by the BAMBI neural network machine-learning package. This is the first study to separate out low-mass isotopes (p, , and He) from the usual light elements (Be, B, C, N, and O). We find that the propagation parameters that best-fit p, , and He data are significantly different from those that fit light elements, including the B/C and 10Be/9Be secondary-to-primary ratios normally used to calibrate propagation parameters. This suggests that each set of species is probing a very different interstellar medium, and that the standard approach of calibrating propagation parameters using B/C can lead to incorrect results. We present posterior distributions and best-fit parameters for propagation of both sets of nuclei, as well as for the injection abundances of elements from H to Si. The input GALDEF files with these new parameters will be included in an upcoming public GALPROP update.

Bayesian analysis of hydrological time series based on MCMC algorithm

In this paper we consider Bayesian analysis of the possible changes in hydrological time series by Markov chain Monte Carlo (MCMC) algorithm. We consider multiple change-points and various possible situations. The approach of Bayesian stochastic search selection is used for detecting and estimating the number and positions of possible change-point in a piecewise constant model. MCMC algorithm is used to estimate the posterior distributions of parameters. The result of the analysis is applied to the hydrological data sets of the major river net area of Shunde in China and the data set of Nile River. In order to further investigate the trends in each segment of the hydrological data sets, we consider the analysis of change-point regression model via MCMC algorithm.

Modeling Causal Relationship Between Brain Regions Within the Drug-Cue Processing Network in Chronic Cocaine Smokers

The cues associated with drugs of abuse have an essential role in perpetuating problematic use, yet effective connectivity or the causal interaction between brain regions mediating the processing of drug cues has not been defined. The aim of this fMRI study was to model the causal interaction between brain regions within the drug-cue processing network in chronic cocaine smokers and matched control participants during a cocaine-cue exposure task. Specifically, cocaine-smoking (15M; 5F) and healthy control (13M; 4F) participants viewed cocaine and neutral cues while in the scanner (a Siemens 3 T magnet). We examined whole brain activation, including activation related to drug-cue processing. Time series data extracted from ROIs determined through our General Linear Model (GLM) analysis and prior publications were used as input to IMaGES, a computationally powerful Bayesian search algorithm. During cocaine-cue exposure, cocaine users showed a particular feed-forward effective connectivity pattern between the ROIs of the drug-cue processing network (amygdala → hippocampus → dorsal striatum → insula → medial frontal cortex, dorsolateral prefrontal cortex, anterior cingulate cortex) that was not present when the controls viewed the cocaine cues. Cocaine craving ratings positively correlated with the strength of the causal influence of the insula on the dorsolateral prefrontal cortex in cocaine users. This study is the first demonstration of a causal interaction between ROIs within the drug-cue processing network in cocaine users. This study provides insight into the mechanism underlying continued substance use and has implications for monitoring treatment response.

Planck2013 results. XXVI. Background geometry and topology of the Universe

Planck CMB temperature maps allow detection of large-scale departures from homogeneity and isotropy. We search for topology with a fundamental domain nearly intersecting the last scattering surface (comoving distance $\chi_r$). For most topologies studied the likelihood maximized over orientation shows some preference for multi-connected models just larger than $\chi_r$. This effect is also present in simulated realizations of isotropic maps and we interpret it as the alignment of mild anisotropic correlations with chance features in a single realization; such a feature can also exist, in milder form, when the likelihood is marginalized over orientations. Thus marginalized, the limits on the radius $R_i$ of the largest sphere inscribed in a topological domain (at log-likelihood-ratio -5) are: in a flat Universe, $R_i>0.9\chi_r$ for the cubic torus (cf. $R_i>0.9\chi_r$ at 99% CL for a matched-circles search); $R_i>0.7\chi_r$ for the chimney; $R_i>0.5\chi_r$ for the slab; in a positively curved Universe, $R_i>1.0\chi_r$ for the dodecahedron; $R_i>1.0\chi_r$ for the truncated cube; $R_i>0.9\chi_r$ for the octahedron. Similar limits apply to alternate topologies. We perform a Bayesian search for an anisotropic Bianchi VII$_h$ geometry. In a non-physical setting where the Bianchi parameters are decoupled from cosmology, Planck data favour a Bianchi component with a Bayes factor of at least 1.5 units of log-evidence: a Bianchi pattern is efficient at accounting for some large-scale anomalies in Planck data. However, the cosmological parameters are in strong disagreement with those found from CMB anisotropy data alone. In the physically motivated setting where the Bianchi parameters are fitted simultaneously with standard cosmological parameters, we find no evidence for a Bianchi VII$_h$ cosmology and constrain the vorticity of such models: $(\omega/H)_0<8\times10^{-10}$ (95% CL). [Abridged]

Optimal multiplicative Bayesian search for a lost target

This paper deals with the problem of searching for not evading lost target by using Bayesian approach. The target may be stationary or drifting in one of n-disjoint bounded known regions. We use a team of n-searchers such that each region has a single searcher. The purpose here is to formulate a search model and obtains two candidate utility functions namely the mean time to detection and the cumulative probability of detection for the control solution. Furthermore, we maximize the chances of detecting the target given a restricted amount of time by maximizing probability of detection over the time horizon. The effectiveness of this method is illustrated by using a real world example with numerical results.

Bayesian search for low-mass planets around nearby M dwarfs – estimates for occurrence rate based on global detectability statistics

Due to their higher planet-star mass-ratios, M dwarfs are the easiest targets for detection of low-mass planets orbiting nearby stars using Doppler spectroscopy. Furthermore, because of their low masses and luminosities, Doppler measurements enable the detection of low-mass planets in their habitable zones that correspond to closer orbits than for Solar-type stars. We re-analyse literature UVES radial velocities of 41 nearby M dwarfs in a combination with new velocities obtained from publicly available spectra from the HARPS-ESO spectrograph of these stars in an attempt to constrain any low-amplitude Keplerian signals. We apply Bayesian signal detection criteria, together with posterior sampling techniques, in combination with noise models that take into account correlations in the data and obtain estimates for the number of planet candidates in the sample. More generally, we use the estimated detection probability function to calculate the occurrence rate of low-mass planets around nearby M dwarfs. We report eight new planet candidates in the sample (orbiting GJ 27.1, GJ 160.2, GJ 180, GJ 229, GJ 422, and GJ 682), including two new multiplanet systems, and confirm two previously known candidates in the GJ 433 system based on detections of Keplerian signals in the combined UVES and HARPS radial velocity data that cannot be explained by periodic and/or quasiperiodic phenomena related to stellar activities. Finally, we use the estimated detection probability function to calculate the occurrence rate of low-mass planets around nearby M dwarfs. According to our results, M dwarfs are hosts to an abundance of low-mass planets and the occurrence rate of planets less massive than 10 M$_{\oplus}$ is of the order of one planet per star, possibly even greater. ...