'Bayesian Optimisation for Nurse Scheduling'

A Bayesian optimisation algorithm for a nurse scheduling problem is presented, which involves choosing a suitable scheduling rule from a set for each nurse's assignment. When a human scheduler works, he normally builds a schedule systematically following a set of rules. After much practice, the scheduler gradually masters the knowledge of which solution parts go well with others. He can identify good parts and is aware of the solution quality even if the scheduling process is not yet completed, thus having the ability to finish a schedule by using flexible, rather than fixed, rules. In this paper, we design a more human-like scheduling algorithm, by using a Bayesian optimisation algorithm to implement explicit learning from past solutions. A nurse scheduling problem from a UK hospital is used for testing. Unlike our previous work that used Genetic Algorithms to implement implicit learning [1], the learning in the proposed algorithm is explicit, i.e. we identify and mix building blocks directly. The Bayesian optimisation algorithm is applied to implement such explicit learning by building a Bayesian network of the joint distribution of solutions. The conditional probability of each variable in the network is computed according to an initial set of promising solutions. Subsequently, each new instance for each variable is generated by using the corresponding conditional probabilities, until all variables have been generated, i.e. in our case, new rule strings have been obtained. Sets of rule strings are generated in this way, some of which will replace previous strings based on fitness. If stopping conditions are not met, the conditional probabilities for all nodes in the Bayesian network are updated again using the current set of promising rule strings. For clarity, consider the following toy example of scheduling five nurses with two rules (1: random allocation, 2: allocate nurse to low-cost shifts). In the beginning of the search, the probabilities of choosing rule 1 or 2 for each nurse is equal, i.e. 50%. After a few iterations, due to the selection pressure and reinforcement learning, we experience two solution pathways: Because pure low-cost or random allocation produces low quality solutions, either rule 1 is used for the first 2-3 nurses and rule 2 on remainder or vice versa. In essence, Bayesian network learns 'use rule 2 after 2-3x using rule 1' or vice versa. It should be noted that for our and most other scheduling problems, the structure of the network model is known and all variables are fully observed. In this case, the goal of learning is to find the rule values that maximize the likelihood of the training data. Thus, learning can amount to 'counting' in the case of multinomial distributions. For our problem, we use our rules: Random, Cheapest Cost, Best Cover and Balance of Cost and Cover. In more detail, the steps of our Bayesian optimisation algorithm for nurse scheduling are: 1. Set t = 0, and generate an initial population P(0) at random; 2. Use roulette-wheel selection to choose a set of promising rule strings S(t) from P(t); 3. Compute conditional probabilities of each node according to this set of promising solutions; 4. Assign each nurse using roulette-wheel selection based on the rules' conditional probabilities. A set of new rule strings O(t) will be generated in this way; 5. Create a new population P(t+1) by replacing some rule strings from P(t) with O(t), and set t = t+1; 6. If the termination conditions are not met (we use 2000 generations), go to step 2. Computational results from 52 real data instances demonstrate the success of this approach. They also suggest that the learning mechanism in the proposed approach might be suitable for other scheduling problems. Another direction for further research is to see if there is a good constructing sequence for individual data instances, given a fixed nurse scheduling order. If so, the good patterns could be recognized and then extracted as new domain knowledge. Thus, by using this extracted knowledge, we can assign specific rules to the corresponding nurses beforehand, and only schedule the remaining nurses with all available rules, making it possible to reduce the solution space. Acknowledgements The work was funded by the UK Government's major funding agency, Engineering and Physical Sciences Research Council (EPSRC), under grand GR/R92899/01. References [1] Aickelin U, "An Indirect Genetic Algorithm for Set Covering Problems", Journal of the Operational Research Society, 53(10): 1118-1126,

A flexible bio-inspired hierarchical model for analyzing musical timbre

A flexible and multipurpose bio-inspired hierarchical model for analyzing musical timbre is presented in this paper. Inspired by findings in the fields of neuroscience, computational neuroscience, and psychoacoustics, not only does the model extract spectral and temporal characteristics of a signal, but it also analyzes amplitude modulations on different timescales. It uses a cochlear filter bank to resolve the spectral components of a sound, lateral inhibition to enhance spectral resolution, and a modulation filter bank to extract the global temporal envelope and roughness of the sound from amplitude modulations. The model was evaluated in three applications. First, it was used to simulate subjective data from two roughness experiments. Second, it was used for musical instrument classification using the k-NN algorithm and a Bayesian network. Third, it was applied to find the features that characterize sounds whose timbres were labeled in an audiovisual experiment. The successful application of the proposed model in these diverse tasks revealed its potential in capturing timbral information.

'Bayesian Optimisation for Nurse Scheduling'

A Bayesian optimisation algorithm for a nurse scheduling problem is presented, which involves choosing a suitable scheduling rule from a set for each nurse's assignment. When a human scheduler works, he normally builds a schedule systematically following a set of rules. After much practice, the scheduler gradually masters the knowledge of which solution parts go well with others. He can identify good parts and is aware of the solution quality even if the scheduling process is not yet completed, thus having the ability to finish a schedule by using flexible, rather than fixed, rules. In this paper, we design a more human-like scheduling algorithm, by using a Bayesian optimisation algorithm to implement explicit learning from past solutions. A nurse scheduling problem from a UK hospital is used for testing. Unlike our previous work that used Genetic Algorithms to implement implicit learning [1], the learning in the proposed algorithm is explicit, i.e. we identify and mix building blocks directly. The Bayesian optimisation algorithm is applied to implement such explicit learning by building a Bayesian network of the joint distribution of solutions. The conditional probability of each variable in the network is computed according to an initial set of promising solutions. Subsequently, each new instance for each variable is generated by using the corresponding conditional probabilities, until all variables have been generated, i.e. in our case, new rule strings have been obtained. Sets of rule strings are generated in this way, some of which will replace previous strings based on fitness. If stopping conditions are not met, the conditional probabilities for all nodes in the Bayesian network are updated again using the current set of promising rule strings. For clarity, consider the following toy example of scheduling five nurses with two rules (1: random allocation, 2: allocate nurse to low-cost shifts). In the beginning of the search, the probabilities of choosing rule 1 or 2 for each nurse is equal, i.e. 50%. After a few iterations, due to the selection pressure and reinforcement learning, we experience two solution pathways: Because pure low-cost or random allocation produces low quality solutions, either rule 1 is used for the first 2-3 nurses and rule 2 on remainder or vice versa. In essence, Bayesian network learns 'use rule 2 after 2-3x using rule 1' or vice versa. It should be noted that for our and most other scheduling problems, the structure of the network model is known and all variables are fully observed. In this case, the goal of learning is to find the rule values that maximize the likelihood of the training data. Thus, learning can amount to 'counting' in the case of multinomial distributions. For our problem, we use our rules: Random, Cheapest Cost, Best Cover and Balance of Cost and Cover. In more detail, the steps of our Bayesian optimisation algorithm for nurse scheduling are: 1. Set t = 0, and generate an initial population P(0) at random; 2. Use roulette-wheel selection to choose a set of promising rule strings S(t) from P(t); 3. Compute conditional probabilities of each node according to this set of promising solutions; 4. Assign each nurse using roulette-wheel selection based on the rules' conditional probabilities. A set of new rule strings O(t) will be generated in this way; 5. Create a new population P(t+1) by replacing some rule strings from P(t) with O(t), and set t = t+1; 6. If the termination conditions are not met (we use 2000 generations), go to step 2. Computational results from 52 real data instances demonstrate the success of this approach. They also suggest that the learning mechanism in the proposed approach might be suitable for other scheduling problems. Another direction for further research is to see if there is a good constructing sequence for individual data instances, given a fixed nurse scheduling order. If so, the good patterns could be recognized and then extracted as new domain knowledge. Thus, by using this extracted knowledge, we can assign specific rules to the corresponding nurses beforehand, and only schedule the remaining nurses with all available rules, making it possible to reduce the solution space. Acknowledgements The work was funded by the UK Government's major funding agency, Engineering and Physical Sciences Research Council (EPSRC), under grand GR/R92899/01. References [1] Aickelin U, "An Indirect Genetic Algorithm for Set Covering Problems", Journal of the Operational Research Society, 53(10): 1118-1126,

Chatter avoidance in the milling of thin floors with bull-nose end mills: Model and stability diagrams

The milling of thin parts is a high added value operation where the machinist has to face the chatter problem. The study of the stability of these operations is a complex task due to the changing modal parameters as the part loses mass during the machining and the complex shape of the tools that are used. The present work proposes a methodology for chatter avoidance in the milling of flexible thin floors with a bull-nose end mill. First, a stability model for the milling of compliant systems in the tool axis direction with bull-nose end mills is presented. The contribution is the averaging method used to be able to use a linear model to predict the stability of the operation. Then, the procedure for the calculation of stability diagrams for the milling of thin floors is presented. The method is based on the estimation of the modal parameters of the part and the corresponding stability lobes during the machining. As in thin floor milling the depth of cut is already defined by the floor thickness previous to milling, the use of stability diagrams that relate the tool position along the tool-path with the spindle speed is proposed. Hence, the sequence of spindle speeds that the tool must have during the milling can be selected. Finally, this methodology has been validated by means of experimental tests.

A Bayesian network dealing with measurements and residuals for system monitoring

International audience

Ensemble Stream Model for Data-Cleaning in Sensor Networks

Ensemble Stream Modeling and Data-cleaning are sensor information processing systems have different training and testing methods by which their goals are cross-validated. This research examines a mechanism, which seeks to extract novel patterns by generating ensembles from data. The main goal of label-less stream processing is to process the sensed events to eliminate the noises that are uncorrelated, and choose the most likely model without over fitting thus obtaining higher model confidence. Higher quality streams can be realized by combining many short streams into an ensemble which has the desired quality. The framework for the investigation is an existing data mining tool. First, to accommodate feature extraction such as a bush or natural forest-fire event we make an assumption of the burnt area (BA*), sensed ground truth as our target variable obtained from logs. Even though this is an obvious model choice the results are disappointing. The reasons for this are two: One, the histogram of fire activity is highly skewed. Two, the measured sensor parameters are highly correlated. Since using non descriptive features does not yield good results, we resort to temporal features. By doing so we carefully eliminate the averaging effects; the resulting histogram is more satisfactory and conceptual knowledge is learned from sensor streams. Second is the process of feature induction by cross-validating attributes with single or multi-target variables to minimize training error. We use F-measure score, which combines precision and accuracy to determine the false alarm rate of fire events. The multi-target data-cleaning trees use information purity of the target leaf-nodes to learn higher order features. A sensitive variance measure such as f-test is performed during each node’s split to select the best attribute. Ensemble stream model approach proved to improve when using complicated features with a simpler tree classifier. The ensemble framework for data-cleaning and the enhancements to quantify quality of fitness (30% spatial, 10% temporal, and 90% mobility reduction) of sensor led to the formation of streams for sensor-enabled applications. Which further motivates the novelty of stream quality labeling and its importance in solving vast amounts of real-time mobile streams generated today.

Dynamic Bayesian network for semantic place classification in mobile robotics

In this paper, the problem of semantic place categorization in mobile robotics is addressed by considering a time-based probabilistic approach called dynamic Bayesian mixture model (DBMM), which is an improved variation of the dynamic Bayesian network. More specifically, multi-class semantic classification is performed by a DBMM composed of a mixture of heterogeneous base classifiers, using geometrical features computed from 2D laserscanner data, where the sensor is mounted on-board a moving robot operating indoors. Besides its capability to combine different probabilistic classifiers, the DBMM approach also incorporates time-based (dynamic) inferences in the form of previous class-conditional probabilities and priors. Extensive experiments were carried out on publicly available benchmark datasets, highlighting the influence of the number of time-slices and the effect of additive smoothing on the classification performance of the proposed approach. Reported results, under different scenarios and conditions, show the effectiveness and competitive performance of the DBMM.

A Bayesian approach to study the risk variables for tuberculosis occurrence in domestic and wild ungulates in South Central Spain

BACKGROUND Bovine tuberculosis (bTB) is a chronic infectious disease mainly caused by Mycobacterium bovis. Although eradication is a priority for the European authorities, bTB remains active or even increasing in many countries, causing significant economic losses. The integral consideration of epidemiological factors is crucial to more cost-effectively allocate control measures. The aim of this study was to identify the nature and extent of the association between TB distribution and a list of potential risk factors regarding cattle, wild ungulates and environmental aspects in Ciudad Real, a Spanish province with one of the highest TB herd prevalences. RESULTS We used a Bayesian mixed effects multivariable logistic regression model to predict TB occurrence in either domestic or wild mammals per municipality in 2007 by using information from the previous year. The municipal TB distribution and endemicity was clustered in the western part of the region and clearly overlapped with the explanatory variables identified in the final model: (1) incident cattle farms, (2) number of years of veterinary inspection of big game hunting events, (3) prevalence in wild boar, (4) number of sampled cattle, (5) persistent bTB-infected cattle farms, (6) prevalence in red deer, (7) proportion of beef farms, and (8) farms devoted to bullfighting cattle. CONCLUSIONS The combination of these eight variables in the final model highlights the importance of the persistence of the infection in the hosts, surveillance efforts and some cattle management choices in the circulation of M. bovis in the region. The spatial distribution of these variables, together with particular Mediterranean features that favour the wildlife-livestock interface may explain the M. bovis persistence in this region. Sanitary authorities should allocate efforts towards specific areas and epidemiological situations where the wildlife-livestock interface seems to critically hamper the definitive bTB eradication success.

Assessment of the sensitivity and specificity of serological (IFAT) and molecular (direct PCR) techniques for diagnosis of leishmaniasis in lagomorphs using a Bayesian approach

Leishmaniasis, caused by Leishmania infantum, is a vector-borne zoonotic disease that is endemic to the Mediterranean basin. The potential of rabbits and hares to serve as competent reservoirs for the disease has recently been demonstrated, although assessment of the importance of their role on disease dynamics is hampered by the absence of quantitative knowledge on the accuracy of diagnostic techniques in these species. A Bayesian latent-class model was used here to estimate the sensitivity and specificity of the Immuno-fluorescence antibody test (IFAT) in serum and a Leishmania-nested PCR (Ln-PCR) in skin for samples collected from 217 rabbits and 70 hares from two different populations in the region of Madrid, Spain. A two-population model, assuming conditional independence between test results and incorporating prior information on the performance of the tests in other animal species obtained from the literature, was used. Two alternative cut-off values were assumed for the interpretation of the IFAT results: 1/50 for conservative and 1/25 for sensitive interpretation. Results suggest that sensitivity and specificity of the IFAT were around 70–80%, whereas the Ln-PCR was highly specific (96%) but had a limited sensitivity (28.9% applying the conservative interpretation and 21.3% with the sensitive one). Prevalence was higher in the rabbit population (50.5% and 72.6%, for the conservative and sensitive interpretation, respectively) than in hares (6.7% and 13.2%). Our results demonstrate that the IFAT may be a useful screening tool for diagnosis of leishmaniasis in rabbits and hares. These results will help to design and implement surveillance programmes in wild species, with the ultimate objective of early detecting and preventing incursions of the disease into domestic and human populations.

Breaking the curve with candels: a Bayesian approach to reveal the non-universality of the dust-attenuation law at high redshift

Dust attenuation affects nearly all observational aspects of galaxy evolution, yet very little is known about the form of the dust-attenuation law in the distant universe. Here, we model the spectral energy distributions of galaxies at z ~ 1.5–3 from CANDELS with rest-frame UV to near-IR imaging under different assumptions about the dust law, and compare the amount of inferred attenuated light with the observed infrared (IR) luminosities. Some individual galaxies show strong Bayesian evidence in preference of one dust law over another, and this preference agrees with their observed location on the plane of infrared excess (IRX, L_TIR/L_UV) and UV slope (β). We generalize the shape of the dust law with an empirical model, A_ λ,σ =E(B-V)k_ λ (λ / λ v)^ σ where k_λ is the dust law of Calzetti et al., and show that there exists a correlation between the color excess E(B-V) and tilt δ with δ =(0.62±0.05)log(E(B-V))+(0.26±0.02). Galaxies with high color excess have a shallower, starburst-like law, and those with low color excess have a steeper, SMC-like law. Surprisingly, the galaxies in our sample show no correlation between the shape of the dust law and stellar mass, star formation rate, or β. The change in the dust law with color excess is consistent with a model where attenuation is caused by scattering, a mixed star–dust geometry, and/or trends with stellar population age, metallicity, and dust grain size. This rest-frame UV-to-near-IR method shows potential to constrain the dust law at even higher redshifts (z>3).

Sparse hierarchical Bayesian models for detecting relevant antigenic sites in virus evolution

Understanding how virus strains offer protection against closely related emerging strains is vital for creating effective vaccines. For many viruses, including Foot-and-Mouth Disease Virus (FMDV) and the Influenza virus where multiple serotypes often co-circulate, in vitro testing of large numbers of vaccines can be infeasible. Therefore the development of an in silico predictor of cross-protection between strains is important to help optimise vaccine choice. Vaccines will offer cross-protection against closely related strains, but not against those that are antigenically distinct. To be able to predict cross-protection we must understand the antigenic variability within a virus serotype, distinct lineages of a virus, and identify the antigenic residues and evolutionary changes that cause the variability. In this thesis we present a family of sparse hierarchical Bayesian models for detecting relevant antigenic sites in virus evolution (SABRE), as well as an extended version of the method, the extended SABRE (eSABRE) method, which better takes into account the data collection process. The SABRE methods are a family of sparse Bayesian hierarchical models that use spike and slab priors to identify sites in the viral protein which are important for the neutralisation of the virus. In this thesis we demonstrate how the SABRE methods can be used to identify antigenic residues within different serotypes and show how the SABRE method outperforms established methods, mixed-effects models based on forward variable selection or l1 regularisation, on both synthetic and viral datasets. In addition we also test a number of different versions of the SABRE method, compare conjugate and semi-conjugate prior specifications and an alternative to the spike and slab prior; the binary mask model. We also propose novel proposal mechanisms for the Markov chain Monte Carlo (MCMC) simulations, which improve mixing and convergence over that of the established component-wise Gibbs sampler. The SABRE method is then applied to datasets from FMDV and the Influenza virus in order to identify a number of known antigenic residue and to provide hypotheses of other potentially antigenic residues. We also demonstrate how the SABRE methods can be used to create accurate predictions of the important evolutionary changes of the FMDV serotypes. In this thesis we provide an extended version of the SABRE method, the eSABRE method, based on a latent variable model. The eSABRE method takes further into account the structure of the datasets for FMDV and the Influenza virus through the latent variable model and gives an improvement in the modelling of the error. We show how the eSABRE method outperforms the SABRE methods in simulation studies and propose a new information criterion for selecting the random effects factors that should be included in the eSABRE method; block integrated Widely Applicable Information Criterion (biWAIC). We demonstrate how biWAIC performs equally to two other methods for selecting the random effects factors and combine it with the eSABRE method to apply it to two large Influenza datasets. Inference in these large datasets is computationally infeasible with the SABRE methods, but as a result of the improved structure of the likelihood, we are able to show how the eSABRE method offers a computational improvement, leading it to be used on these datasets. The results of the eSABRE method show that we can use the method in a fully automatic manner to identify a large number of antigenic residues on a variety of the antigenic sites of two Influenza serotypes, as well as making predictions of a number of nearby sites that may also be antigenic and are worthy of further experiment investigation.

Genetic parameters for carcass traits and body weight using a Bayesian approach in the Canchim cattle.

Correlation between genetic parameters and factors such as backfat thickness (BFT), rib eye area (REA), and body weight (BW) were estimated for Canchim beef cattle raised in natural pastures of Brazil. Data from 1648 animals were analyzed using multi-trait (BFT, REA, and BW) animal models by the Bayesian approach. This model included the effects of contemporary group, age, and individual heterozygosity as covariates. In addition, direct additive genetic and random residual effects were also analyzed. Heritability estimated for BFT (0.16), REA (0.50), and BW (0.44) indicated their potential for genetic improvements and response to selection processes. Furthermore, genetic correlations between BW and the remaining traits were high (P > 0.50), suggesting that selection for BW could improve REA and BFT. On the other hand, genetic correlation between BFT and REA was low (P = 0.39 ± 0.17), and included considerable variations, suggesting that these traits can be jointly included as selection criteria without influencing each other. We found that REA and BFT responded to the selection processes, as measured by ultrasound. Therefore, selection for yearling weight results in changes in REA and BFT.

A Trans-dimensional inversion algorithm to model deformation sources with unconstrained shape in finite element domains

Ground deformation provides valuable insights on subsurface processes with pattens reflecting the characteristics of the source at depth. In active volcanic sites displacements can be observed in unrest phases; therefore, a correct interpretation is essential to assess the hazard potential. Inverse modeling is employed to obtain quantitative estimates of parameters describing the source. However, despite the robustness of the available approaches, a realistic imaging of these reservoirs is still challenging. While analytical models return quick but simplistic results, assuming an isotropic and elastic crust, more sophisticated numerical models, accounting for the effects of topographic loads, crust inelasticity and structural discontinuities, require much higher computational effort and information about the crust rheology may be challenging to infer. All these approaches are based on a-priori source shape constraints, influencing the solution reliability. In this thesis, we present a new approach aimed at overcoming the aforementioned limitations, modeling sources free of a-priori shape constraints with the advantages of FEM simulations, but with a cost-efficient procedure. The source is represented as an assembly of elementary units, consisting in cubic elements of a regular FE mesh loaded with a unitary stress tensors. The surface response due to each of the six stress tensor components is computed and linearly combined to obtain the total displacement field. In this way, the source can assume potentially any shape. Our tests prove the equivalence of the deformation fields due to our assembly and that of corresponding cavities with uniform boundary pressure. Our ability to simulate pressurized cavities in a continuum domain permits to pre-compute surface responses, avoiding remeshing. A Bayesian trans-dimensional inversion algorithm implementing this strategy is developed. 3D Voronoi cells are used to sample the model domain, selecting the elementary units contributing to the source solution and those remaining inactive as part of the crust.

Integrated Proteomics Identified Up-regulated Focal Adhesion-mediated Proteins In Human Squamous Cell Carcinoma In An Orthotopic Murine Model.

Understanding the molecular mechanisms of oral carcinogenesis will yield important advances in diagnostics, prognostics, effective treatment, and outcome of oral cancer. Hence, in this study we have investigated the proteomic and peptidomic profiles by combining an orthotopic murine model of oral squamous cell carcinoma (OSCC), mass spectrometry-based proteomics and biological network analysis. Our results indicated the up-regulation of proteins involved in actin cytoskeleton organization and cell-cell junction assembly events and their expression was validated in human OSCC tissues. In addition, the functional relevance of talin-1 in OSCC adhesion, migration and invasion was demonstrated. Taken together, this study identified specific processes deregulated in oral cancer and provided novel refined OSCC-targeting molecules.

Electronic And Structural Study Of Pt-modified Au Vicinal Surfaces: A Model System For Pt-au Catalysts.

Two single crystalline surfaces of Au vicinal to the (111) plane were modified with Pt and studied using scanning tunneling microscopy (STM) and X-ray photoemission spectroscopy (XPS) in ultra-high vacuum environment. The vicinal surfaces studied are Au(332) and Au(887) and different Pt coverage (θPt) were deposited on each surface. From STM images we determine that Pt deposits on both surfaces as nanoislands with heights ranging from 1 ML to 3 ML depending on θPt. On both surfaces the early growth of Pt ad-islands occurs at the lower part of the step edge, with Pt ad-atoms being incorporated into the steps in some cases. XPS results indicate that partial alloying of Pt occurs at the interface at room temperature and at all coverage, as suggested by the negative chemical shift of Pt 4f core line, indicating an upward shift of the d-band center of the alloyed Pt. Also, the existence of a segregated Pt phase especially at higher coverage is detected by XPS. Sample annealing indicates that the temperature rise promotes a further incorporation of Pt atoms into the Au substrate as supported by STM and XPS results. Additionally, the catalytic activity of different PtAu systems reported in the literature for some electrochemical reactions is discussed considering our findings.