Uncertainty
Best-First Enumeration Based on Bounding Conflicts, and its Application to Large-scale Hybrid Estimation
Timmons, Eric Michael (MIT) | Williams, Brian Charles (MIT)
There is an increasing desire for autonomous systems to have high levels of robustness and safety, attained through continuously planning and self-repairing online. Underlying this is the need to accurately estimate the system state and diagnose subtle failures. Estimation methods based on hybrid discrete and continuous state models have emerged as a method of precisely computing these estimates. However, existing methods have difficulty scaling to systems with more than a handful of components. Discrete, consistency based state estimation capabilities can scale to this level by combining best-first enumeration and conflict-directed search. While best-first methods have been developed for hybrid estimation, conflict-directed methods have thus far been elusive as conflicts learn inconsistencies from constraint violation, but probabilistic hybrid estimation is relatively unconstrained. In this paper we present an approach to hybrid estimation that unifies best-first enumeration and conflict-directed search through the concept of "bounding" conflicts, an extension of conflicts that represent tighter bounds on the cost of regions of the search space. This paper presents a general best-first enumeration algorithm based on bounding conflicts (A*BC) and a hybrid estimation method using this enumeration algorithm. Experiments show that an A*BC powered state estimator produces estimates up to an order of magnitude faster than the current state of the art, particularly on large systems.
Reproducible Bootstrap Aggregating
Heterogeneity between training and testing data degrades reproducibility of a well-trained predictive algorithm. In modern applications, how to deploy a trained algorithm in a different domain is becoming an urgent question raised by many domain scientists. In this paper, we propose a reproducible bootstrap aggregating (Rbagging) method coupled with a new algorithm, the iterative nearest neighbor sampler (INNs), effectively drawing bootstrap samples from training data to mimic the distribution of the test data. Rbagging is a general ensemble framework that can be applied to most classifiers. We further propose Rbagging+ to effectively detect anomalous samples in the testing data. Our theoretical results show that the resamples based on Rbagging have the same distribution as the testing data. Moreover, under suitable assumptions, we further provide a general bound to control the test excess risk of the ensemble classifiers. The proposed method is compared with several other popular domain adaptation methods via extensive simulation studies and real applications including medical diagnosis and imaging classifications.
Unbiased and Efficient Log-Likelihood Estimation with Inverse Binomial Sampling
van Opheusden, Bas, Acerbi, Luigi, Ma, Wei Ji
The fate of scientific hypotheses often relies on the ability of a computational model to explain the data, quantified in modern statistical approaches by the likelihood function. The log-likelihood is the key element for parameter estimation and model evaluation. However, the log-likelihood of complex models in fields such as computational biology and neuroscience is often intractable to compute analytically or numerically. In those cases, researchers can often only estimate the log-likelihood by comparing observed data with synthetic observations generated by model simulations. Standard techniques to approximate the likelihood via simulation either use summary statistics of the data or are at risk of producing severe biases in the estimate. Here, we explore another method, inverse binomial sampling (IBS), which can estimate the log-likelihood of an entire data set efficiently and without bias. For each observation, IBS draws samples from the simulator model until one matches the observation. The log-likelihood estimate is then a function of the number of samples drawn. The variance of this estimator is uniformly bounded, achieves the minimum variance for an unbiased estimator, and we can compute calibrated estimates of the variance. We provide theoretical arguments in favor of IBS and an empirical assessment of the method for maximum-likelihood estimation with simulation-based models. As case studies, we take three model-fitting problems of increasing complexity from computational and cognitive neuroscience. In all problems, IBS generally produces lower error in the estimated parameters and maximum log-likelihood values than alternative sampling methods with the same average number of samples. Our results demonstrate the potential of IBS as a practical, robust, and easy to implement method for log-likelihood evaluation when exact techniques are not available.
Probabilistic Reasoning across the Causal Hierarchy
Ibeling, Duligur, Icard, Thomas
We propose a formalization of the three-tier causal hierarchy of association, intervention, and counterfactuals as a series of probabilistic logical languages. Our languages are of strictly increasing expressivity, the first capable of expressing quantitative probabilistic reasoning---including conditional independence and Bayesian inference---the second encoding do-calculus reasoning for causal effects, and the third capturing a fully expressive do-calculus for arbitrary counterfactual queries. We give a corresponding series of finitary axiomatizations complete over both structural causal models and probabilistic programs, and show that satisfiability and validity for each language are decidable in polynomial space.
Modeling Climate Change Impact on Wind Power Resources Using Adaptive Neuro-Fuzzy Inference System
Nabipour, Narjes, Mosavi, Amir, Hajnal, Eva, Nadai, Laszlo, Shamshirband, Shahab, Chau, Kwok-Wing
Climate change impacts and adaptations are the subjects to ongoing issues that attract the attention of many researchers. Insight into the wind power potential in an area and its probable variation due to climate change impacts can provide useful information for energy policymakers and strategists for sustainable development and management of the energy. In this study, spatial variation of wind power density at the turbine hub-height and its variability under future climatic scenarios are taken under consideration. An ANFIS based post-processing technique was employed to match the power outputs of the regional climate model with those obtained from the reference data. The near-surface wind data obtained from a regional climate model are employed to investigate climate change impacts on the wind power resources in the Caspian Sea. Subsequent to converting near-surface wind speed to turbine hub-height speed and computation of wind power density, the results have been investigated to reveal mean annual power, seasonal, and monthly variability for a 20-year period in the present (1981-2000) and in the future (2081-2100). The findings of this study indicated that the middle and northern parts of the Caspian Sea are placed with the highest values of wind power. However, the results of the post-processing technique using adaptive neuro-fuzzy inference system (ANFIS) model showed that the real potential of the wind power in the area is lower than those of projected from the regional climate model.
An improved online learning algorithm for general fuzzy min-max neural network
Khuat, Thanh Tung, Chen, Fang, Gabrys, Bogdan
An improved online learning algorithm for general fuzzy min-max neural network Thanh Tung Khuat Advanced Analytics Institute University of T echnology Sydney Sydney, Australia thanhtung.khuat@student.uts.edu.au Abstract --This paper proposes an improved version of the current online learning algorithm for a general fuzzy min-max neural network (GFMM) to tackle existing issues concerning expansion and contraction steps as well as the way of dealing with unseen data located on decision boundaries. These drawbacks lower its classification performance, so an improved algorithm is proposed in this study to address the above limitations. The proposed approach does not use the contraction process for overlapping hyperboxes, which is more likely to increase the error rate as shown in the literature. The empirical results indicated the improvement in the classification accuracy and stability of the proposed method compared to the original version and other fuzzy min-max classifiers. In order to reduce the sensitivity to the training samples presentation order of this new online learning algorithm, a simple ensemble method is also proposed. I NTRODUCTION Artificial neural networks (ANNs) are one of the most widely used methods for dealing with classification problems as well as real-world applications [1]. However, the main disadvantage of the original ANNs is that they do not have the capability of giving explanations of their predictive results to humans explicitly. This drawback restricts the widespread use of the ANNs for critical domains such as healthcare and criminal justice [2]. In a recent study, Rudin [2] has highlighted that there is a high demand for interpretable models to substitute black-box models in assisting decision-makers in areas with the requirement of high safety and trust.
Lifted Hybrid Variational Inference
Chen, Yuqiao, Yang, Yibo, Natarajan, Sriraam, Ruozzi, Nicholas
A variety of lifted inference algorithms, which exploit model symmetry to reduce computational cost, have been proposed to render inference tractable in probabilistic relational models. Most existing lifted inference algorithms operate only over discrete domains or continuous domains with restricted potential functions, e.g., Gaussian. We investigate two approximate lifted variational approaches that are applicable to hybrid domains and expressive enough to capture multi-modality. We demonstrate that the proposed variational methods are both scalable and can take advantage of approximate model symmetries, even in the presence of a large amount of continuous evidence. We demonstrate that our approach compares favorably against existing message-passing based approaches in a variety of settings. Finally, we present a sufficient condition for the Bethe approximation to yield a non-trivial estimate over the marginal polytope.
Learning Generative Models using Denoising Density Estimators
Bigdeli, Siavash A., Lin, Geng, Portenier, Tiziano, Dunbar, L. Andrea, Zwicker, Matthias
Learning generative probabilistic models that can estimate the continuous density given a set of samples, and that can sample from that density, is one of the fundamental challenges in unsupervised machine learning. In this paper we introduce a new approach to obtain such models based on what we call denoising density estimators (DDEs). A DDE is a scalar function, parameterized by a neural network, that is efficiently trained to represent a kernel density estimator of the data. Leveraging DDEs, our main contribution is to develop a novel approach to obtain generative models that sample from given densities. We prove that our algorithms to obtain both DDEs and generative models are guaranteed to converge to the correct solutions. Advantages of our approach include that we do not require specific network architectures like in normalizing flows, ordinary differential equation solvers as in continuous normalizing flows, nor do we require adversarial training as in generative adversarial networks (GANs). Finally, we provide experimental results that demonstrate practical applications of our technique.
A Correspondence Analysis Framework for Author-Conference Recommendations
Iyer, Rahul Radhakrishnan, Sharma, Manish, Saradhi, Vijaya
For many years, achievements and discoveries made by scientists are made aware through research papers published in appropriate journals or conferences. Often, established scientists and especially newbies are caught up in the dilemma of choosing an appropriate conference to get their work through. Every scientific conference and journal is inclined towards a particular field of research and there is a vast multitude of them for any particular field. Choosing an appropriate venue is vital as it helps in reaching out to the right audience and also to further one's chance of getting their paper published. In this work, we address the problem of recommending appropriate conferences to the authors to increase their chances of acceptance. We present three different approaches for the same involving the use of social network of the authors and the content of the paper in the settings of dimensionality reduction and topic modeling. In all these approaches, we apply Correspondence Analysis (CA) to derive appropriate relationships between the entities in question, such as conferences and papers. Our models show promising results when compared with existing methods such as content-based filtering, collaborative filtering and hybrid filtering.