Uncertainty
Novelty-organizing team of classifiers in noisy and dynamic environments
Vargas, Danilo Vasconcellos, Takano, Hirotaka, Murata, Junichi
In the real world, the environment is constantly changing with the input variables under the effect of noise. However, few algorithms were shown to be able to work under those circumstances. Here, Novelty-Organizing Team of Classifiers (NOTC) is applied to the continuous action mountain car as well as two variations of it: a noisy mountain car and an unstable weather mountain car. These problems take respectively noise and change of problem dynamics into account. Moreover, NOTC is compared with NeuroEvolution of Augmenting Topologies (NEAT) in these problems, revealing a trade-off between the approaches. While NOTC achieves the best performance in all of the problems, NEAT needs less trials to converge. It is demonstrated that NOTC achieves better performance because of its division of the input space (creating easier problems). Unfortunately, this division of input space also requires a bit of time to bootstrap.
Predictive Collective Variable Discovery with Deep Bayesian Models
Schรถberl, Markus, Zabaras, Nicholas, Koutsourelakis, Phaedon-Stelios
Extending spatio-temporal scale limitations of models for complex atomistic systems considered in biochemistry and materials science necessitates the development of enhanced sampling methods. The potential acceleration in exploring the configurational space by enhanced sampling methods depends on the choice of collective variables (CVs). In this work, we formulate the discovery of CVs as a Bayesian inference problem and consider the CVs as hidden generators of the full-atomistic trajectory. The ability to generate samples of the fine-scale atomistic configurations using limited training data allows us to compute estimates of observables as well as our probabilistic confidence on them. The methodology is based on emerging methodological advances in machine learning and variational inference. The discovered CVs are related to physicochemical properties which are essential for understanding mechanisms especially in unexplored complex systems. We provide a quantitative assessment of the CVs in terms of their predictive ability for alanine dipeptide (ALA-2) and ALA-15 peptide.
A Bayesian Approach for Inferring Local Causal Structure in Gene Regulatory Networks
Bucur, Ioan Gabriel, van Bussel, Tom, Claassen, Tom, Heskes, Tom
Gene regulatory networks play a crucial role in controlling an organism's biological processes, which is why there is significant interest in developing computational methods that are able to extract their structure from high-throughput genetic data. A typical approach consists of a series of conditional independence tests on the covariance structure meant to progressively reduce the space of possible causal models. We propose a novel efficient Bayesian method for discovering the local causal relationships among triplets of (normally distributed) variables. In our approach, we score the patterns in the covariance matrix in one go and we incorporate the available background knowledge in the form of priors over causal structures. Our method is flexible in the sense that it allows for different types of causal structures and assumptions. We apply the approach to the task of inferring gene regulatory networks by learning regulatory relationships between gene expression levels. We show that our algorithm produces stable and conservative posterior probability estimates over local causal structures that can be used to derive an honest ranking of the most meaningful regulatory relationships. We demonstrate the stability and efficacy of our method both on simulated data and on real-world data from an experiment on yeast.
Is rotation forest the best classifier for problems with continuous features?
Bagnall, A., Bostrom, A., Cawley, G., Flynn, M., Large, J., Lines, J.
Rotation forest is a tree based ensemble that performs transforms on subsets of attributes prior to constructing each tree. We present an empirical comparison of classifiers for problems with only real valued features. We evaluate classifiers from three families of algorithms: support vector machines; tree-based ensembles; and neural networks. We compare classifiers on unseen data based on the quality of the decision rule (using classification error) the ability to rank cases (area under the receiver operator curve) and the probability estimates (using negative log likelihood). We conclude that, in answer to the question posed in the title, yes, rotation forest, is significantly more accurate on average than competing techniques when compared on three distinct sets of datasets. The same pattern of results are observed when tuning classifiers on the train data using a grid search. We investigate why rotation forest does so well by testing whether the characteristics of the data can be used to differentiate classifier performance. We assess the impact of the design features of rotation forest through an ablative study that transforms random forest into rotation forest. We identify the major limitation of rotation forest as its scalability, particularly in number of attributes. To overcome this problem we develop a model to predict the train time of the algorithm and hence propose a contract version of rotation forest where a run time cap {\em a priori}. We demonstrate that on large problems rotation forest can be made an order of magnitude faster without significant loss of accuracy and that there is no real benefit (on average) from tuning the ensemble. We conclude that without any domain knowledge to indicate an algorithm preference, rotation forest should be the default algorithm of choice for problems with continuous attributes.
Comparison between Suitable Priors for Additive Bayesian Networks
Kratzer, Gilles, Furrer, Reinhard, Pittavino, Marta
Additive Bayesian networks are types of graphical models that extend the usual Bayesian generalized linear model to multiple dependent variables through the factorisation of the joint probability distribution of the underlying variables. When fitting an ABN model, the choice of the prior of the parameters is of crucial importance. If an inadequate prior - like a too weakly informative one - is used, data separation and data sparsity lead to issues in the model selection process. In this work a simulation study between two weakly and a strongly informative priors is presented. As weakly informative prior we use a zero mean Gaussian prior with a large variance, currently implemented in the R-package abn. The second prior belongs to the Student's t-distribution, specifically designed for logistic regressions and, finally, the strongly informative prior is again Gaussian with mean equal to true parameter value and a small variance. We compare the impact of these priors on the accuracy of the learned additive Bayesian network in function of different parameters. We create a simulation study to illustrate Lindley's paradox based on the prior choice. We then conclude by highlighting the good performance of the informative Student's t-prior and the limited impact of the Lindley's paradox. Finally, suggestions for further developments are provided.
Leveraging Contact Forces for Learning to Grasp
Merzic, Hamza, Bogdanovic, Miroslav, Kappler, Daniel, Righetti, Ludovic, Bohg, Jeannette
Grasping objects under uncertainty remains an open problem in robotics research. This uncertainty is often due to noisy or partial observations of the object pose or shape. To enable a robot to react appropriately to unforeseen effects, it is crucial that it continuously takes sensor feedback into account. While visual feedback is important for inferring a grasp pose and reaching for an object, contact feedback offers valuable information during manipulation and grasp acquisition. In this paper, we use model-free deep reinforcement learning to synthesize control policies that exploit contact sensing to generate robust grasping under uncertainty. We demonstrate our approach on a multi-fingered hand that exhibits more complex finger coordination than the commonly used two-fingered grippers. We conduct extensive experiments in order to assess the performance of the learned policies, with and without contact sensing. While it is possible to learn grasping policies without contact sensing, our results suggest that contact feedback allows for a significant improvement of grasping robustness under object pose uncertainty and for objects with a complex shape.
Approximate message-passing for convex optimization with non-separable penalties
Manoel, Andre, Krzakala, Florent, Varoquaux, Gaรซl, Thirion, Bertrand, Zdeborovรก, Lenka
We introduce an iterative optimization scheme for convex objectives consisting of a linear loss and a non-separable penalty, based on the expectation-consistent approximation and the vector approximate message-passing (VAMP) algorithm. Specifically, the penalties we approach are convex on a linear transformation of the variable to be determined, a notable example being total variation (TV). We describe the connection between message-passing algorithms -- typically used for approximate inference -- and proximal methods for optimization, and show that our scheme is, as VAMP, similar in nature to the Peaceman-Rachford splitting, with the important difference that stepsizes are set adaptively. Finally, we benchmark the performance of our VAMP-like iteration in problems where TV penalties are useful, namely classification in task fMRI and reconstruction in tomography, and show faster convergence than that of state-of-the-art approaches such as FISTA and ADMM in most settings.
Learning Discrete Bayesian Networks from Continuous Data
Chen, Yi-Chun, Wheeler, Tim Allan, Kochenderfer, Mykel John
Learning Bayesian networks from raw data can help provide insights into the relationships between variables. While real data often contains a mixture of discrete and continuous-valued variables, many Bayesian network structure learning algorithms assume all random variables are discrete. Thus, continuous variables are often discretized when learning a Bayesian network. However, the choice of discretization policy has significant impact on the accuracy, speed, and interpretability of the resulting models. This paper introduces a principled Bayesian discretization method for continuous variables in Bayesian networks with quadratic complexity instead of the cubic complexity of other standard techniques. Empirical demonstrations show that the proposed method is superior to the established minimum description length algorithm. In addition, this paper shows how to incorporate existing methods into the structure learning process to discretize all continuous variables and simultaneously learn Bayesian network structures.
Learning to Address Health Inequality in the United States with a Bayesian Decision Network
Sethi, Tavpritesh, Mittal, Anant, Maheshwari, Shubham, Chugh, Samarth
Life-expectancy is a complex outcome driven by genetic, socio-demographic, environmental and geographic factors. Increasing socio-economic and health disparities in the United States are propagating the longevity-gap, making it a cause for concern. Earlier studies have probed individual factors but an integrated picture to reveal quantifiable actions has been missing. Amidst growing concerns about the further widening of healthcare inequality and differential access created by Artificial Intelligence, it is imperative to explore it's potential for illuminating biases and enabling transparent policy decisions. In this work, we reveal actionable interventions for decreasing the longevity-gap in the United States by analyzing a County-level data resource with healthcare, socio-economic, behavioral, education and demographic features. We learn an ensemble-averaged structure, draw inferences using the joint probability distribution and extend it to a Bayesian Decision Network for identifying policy actions. We draw quantitative estimates for the positive roles of diversity, preventive-care quality and stable-families within the unified framework of our decision network. Finally, we make this analysis and dashboard available as an interactive web-application for enabling users and policy-makers to validate our insights on bridging the longevity-gap and explore the ones beyond reported in this work.
Probabilistic DL Reasoning with Pinpointing Formulas: A Prolog-based Approach
Zese, Riccardo, Bellodi, Elena, Cota, Giuseppe, Lamma, Evelina, Riguzzi, Fabrizio
When modeling real world domains we have to deal with information that is incomplete or that comes from sources with different trust levels. This motivates the need for managing uncertainty in the Semantic Web. To this purpose, we introduced a probabilistic semantics, named DISPONTE, in order to combine description logics with probability theory. The probability of a query can be then computed from the set of its explanations by building a Binary Decision Diagram (BDD). The set of explanations can be found using the tableau algorithm, which has to handle non-determinism. Prolog, with its efficient handling of non-determinism, is suitable for implementing the tableau algorithm. TRILL and TRILLP are systems offering a Prolog implementation of the tableau algorithm. TRILLP builds a pinpointing formula, that compactly represents the set of explanations and can be directly translated into a BDD. Both reasoners were shown to outperform state-of-the-art DL reasoners. In this paper, we present an improvement of TRILLP, named TORNADO, in which the BDD is directly built during the construction of the tableau, further speeding up the overall inference process. An experimental comparison shows the effectiveness of TORNADO. All systems can be tried online in the TRILL on SWISH web application at http://trill.ml.unife.it/.