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 Uncertainty


On Interpretability of Artificial Neural Networks

arXiv.org Artificial Intelligence

Deep learning has achieved great successes in many important areas to dealing with text, images, video, graphs, and so on. However, the black-box nature of deep artificial neural networks has become the primary obstacle to their public acceptance and wide popularity in critical applications such as diagnosis and therapy. Due to the huge potential of deep learning, interpreting neural networks has become one of the most critical research directions. In this paper, we systematically review recent studies in understanding the mechanism of neural networks and shed light on some future directions of interpretability research (This work is still in progress).


Semi-Sequential Probabilistic Model For Indoor Localization Enhancement

arXiv.org Artificial Intelligence

This paper proposes a semi-sequential probabilistic model (SSP) that applies an additional short term memory to enhance the performance of the probabilistic indoor localization. The conventional probabilistic methods normally treat the locations in the database indiscriminately. In contrast, SSP leverages the information of the previous position to determine the probable location since the user's speed in an indoor environment is bounded and locations near the previous one have higher probability than the other locations. Although the SSP utilizes the previous location information, it does not require the exact moving speed and direction of the user. On-site experiments using the received signal strength indicator (RSSI) and channel state information (CSI) fingerprints for localization demonstrate that SSP reduces the maximum error and boosts the performance of existing probabilistic approaches by 25% - 30%.


On Thompson Sampling for Smoother-than-Lipschitz Bandits

arXiv.org Machine Learning

Thompson Sampling is a well established approach to bandit and reinforcement learning problems. However its use in continuum armed bandit problems has received relatively little attention. We provide the first bounds on the regret of Thompson Sampling for continuum armed bandits under weak conditions on the function class containing the true function and sub-exponential observation noise. Our bounds are realised by analysis of the eluder dimension, a recently proposed measure of the complexity of a function class, which has been demonstrated to be useful in bounding the Bayesian regret of Thompson Sampling for simpler bandit problems under sub-Gaussian observation noise. We derive a new bound on the eluder dimension for classes of functions with Lipschitz derivatives, and generalise previous analyses in multiple regards.


Exploring Unknown Universes in Probabilistic Relational Models

arXiv.org Artificial Intelligence

Large probabilistic models are often shaped by a pool of known individuals (a universe) and relations between them. Lifted inference algorithms handle sets of known individuals for tractable inference. Universes may not always be known, though, or may only described by assumptions such as "small universes are more likely". Without a universe, inference is no longer possible for lifted algorithms, losing their advantage of tractable inference. The aim of this paper is to define a semantics for models with unknown universes decoupled from a specific constraint language to enable lifted and thereby, tractable inference. Introduction At the heart of many machine learning algorithms lie large probabilistic models that use random variables (randvars) to describe behaviour or structure hidden in data. After a surge in effective machine learning algorithms, efficient algorithms for inference come into focus to make use of the models learned or to optimise machine learning algorithms further (LeCun 2018). Often, a model is shaped by a pool of known individuals (constants), i.e., a known universe, and relations between them. Handling sets of individuals enables tractable inference (Niepert and V an den Broeck 2014).


Variational Bayesian Methods for Stochastically Constrained System Design Problems

arXiv.org Machine Learning

We study system design problems stated as parameterized stochastic programs with a chance-constraint set. We adopt a Bayesian approach that requires the computation of a posterior predictive integral which is usually intractable. In addition, for the problem to be a well-defined convex program, we must retain the convexity of the feasible set. Consequently, we propose a variational Bayes-based method to approximately compute the posterior predictive integral that ensures tractability and retains the convexity of the feasible set. Under certain regularity conditions, we also show that the solution set obtained using variational Bayes converges to the true solution set as the number of observations tends to infinity. We also provide bounds on the probability of qualifying a true infeasible point (with respect to the true constraints) as feasible under the VB approximation for a given number of samples.


Artificial Intelligence for Social Good: A Survey

arXiv.org Artificial Intelligence

Its impact is drastic and real: Youtube's AIdriven recommendation system would present sports videos for days if one happens to watch a live baseball game on the platform [1]; email writing becomes much faster with machine learning (ML) based auto-completion [2]; many businesses have adopted natural language processing based chatbots as part of their customer services [3]. AI has also greatly advanced human capabilities in complex decision-making processes ranging from determining how to allocate security resources to protect airports [4] to games such as poker [5] and Go [6]. All such tangible and stunning progress suggests that an "AI summer" is happening. As some put it, "AI is the new electricity" [7]. Meanwhile, in the past decade, an emerging theme in the AI research community is the so-called "AI for social good" (AI4SG): researchers aim at developing AI methods and tools to address problems at the societal level and improve the wellbeing of the society.


Making Sense of Reinforcement Learning and Probabilistic Inference

arXiv.org Artificial Intelligence

Reinforcement learning (RL) combines a control problem with statistical estimation: the system dynamics are not known to the agent, but can be learned through experience. A recent line of research casts `RL as inference' and suggests a particular framework to generalize the RL problem as probabilistic inference. Our paper surfaces a key shortcoming in that approach, and clarifies the sense in which RL can be coherently cast as an inference problem. In particular, an RL agent must consider the effects of its actions upon future rewards and observations: the exploration-exploitation tradeoff. In all but the most simple settings, the resulting inference is computationally intractable so that practical RL algorithms must resort to approximation. We demonstrate that the popular `RL as inference' approximation can perform poorly in even very basic problems. However, we show that with a small modification the framework does yield algorithms that can provably perform well, and we show that the resulting algorithm is equivalent to the recently proposed K-learning, which we further connect with Thompson sampling.


Aleatoric and Epistemic Uncertainty with Random Forests

arXiv.org Machine Learning

Due to the steadily increasing relevance of machine learning for practical applications, many of which are coming with safety requirements, the notion of uncertainty has received increasing attention in machine learning research in the last couple of years. In particular, the idea of distinguishing between two important types of uncertainty, often refereed to as aleatoric and epistemic, has recently been studied in the setting of supervised learning. In this paper, we propose to quantify these uncertainties with random forests. More specifically, we show how two general approaches for measuring the learner's aleatoric and epistemic uncertainty in a prediction can be instantiated with decision trees and random forests as learning algorithms in a classification setting. In this regard, we also compare random forests with deep neural networks, which have been used for a similar purpose.


Modeling Uncertainty and Imprecision in Nonmonotonic Reasoning using Fuzzy Numbers

arXiv.org Artificial Intelligence

Modern applications of artificial intelligence in decision support systems, plan generation systems require reasoning with imprecise a nd uncertain information. Logical frameworks based on bivalent reasoning are not suitable for such applications, because the set {0, 1} cannot capture the vagueness or uncertainty of underlying proposition. Though fuzzy log ic-based systems can represent imprecise linguistic information by ascribi ng membership values to attributes (or truth values to propositions) taken fr om the interval 1 [0,1], but this graded valuation becomes inadequate if the p recise membership can not be determined due to some underlying uncerta inty. This uncertainty may arise from lack of complete information or f rom lack of reliability of source of information or lack of unanimity amon g rational agents in a multi-agent reasoning system or from many other reasons . This uncertainty with respect to the assignment of membership degr ees is captured by assigning a range of possible membership values, i.e. by a ssigning an interval.


The Real-World-Weight Cross-Entropy Loss Function: Modeling the Costs of Mislabeling

arXiv.org Artificial Intelligence

In this paper, we propose a new metric to measure goodness-of-fit for classifiers, the Real World Cost function. This metric factors in information about a real world problem, such as financial impact, that other measures like accuracy or F1 do not. This metric is also more directly interpretable for users. To optimize for this metric, we introduce the Real-World- Weight Crossentropy loss function, in both binary and single-label classification variants. Both variants allow direct input of real world costs as weights. For single-label, multicategory classification, our loss function also allows direct penalization of probabilistic false positives, weighted by label, during the training of a machine learning model. We compare the design of our loss function to the binary crossentropy and categorical crossentropy functions, as well as their weighted variants, to discuss the potential for improvement in handling a variety of known shortcomings of machine learning, ranging from imbalanced classes to medical diagnostic error to reinforcement of social bias. We create scenarios that emulate those issues using the MNIST data set and demonstrate empirical results of our new loss function. Finally, we sketch a proof of this function based on Maximum Likelihood Estimation and discuss future directions.