Philosophers writing about the ravens paradox often note that Nicod's Condition (NC) holds given some set of background information, and fails to hold against others, but rarely go any further. That is, it is usually not explored which background information makes NC true or false. The present paper aims to fill this gap. For us, "(objective) background knowledge" is restricted to information that can be expressed as probability events. Any other configuration is regarded as being subjective and a property of the a priori probability distribution. We study NC in two specific settings. In the first case, a complete description of some individuals is known, e.g. one knows of each of a group of individuals whether they are black and whether they are ravens. In the second case, the number of individuals having a particular property is given, e.g. one knows how many ravens or how many black things there are (in the relevant population). While some of the most famous answers to the paradox are measure-dependent, our discussion is not restricted to any particular probability measure. Our most interesting result is that in the second setting, NC violates a simple kind of inductive inference (namely projectability). Since relative to NC, this latter rule is more closely related to, and more directly justified by our intuitive notion of inductive reasoning, this tension makes a case against the plausibility of NC. In the end, we suggest that the informal representation of NC may seem to be intuitively plausible because it can easily be mistaken for reasoning by analogy.

On-line estimation plays an important role in process control and monitoring. Obtaining a theoretical solution to the simultaneous state-parameter estimation problem for non-linear stochastic systems involves solving complex multi-dimensional integrals that are not amenable to analytical solution. While basic sequential Monte-Carlo (SMC) or particle filtering (PF) algorithms for simultaneous estimation exist, it is well recognized that there is a need for making these on-line algorithms non-degenerate, fast and applicable to processes with missing measurements. To overcome the deficiencies in traditional algorithms, this work proposes a Bayesian approach to on-line state and parameter estimation. Its extension to handle missing data in real-time is also provided. The simultaneous estimation is performed by filtering an extended vector of states and parameters using an adaptive sequential-importance-resampling (SIR) filter with a kernel density estimation method. The approach uses an on-line optimization algorithm based on Kullback-Leibler (KL) divergence to allow adaptation of the SIR filter for combined state-parameter estimation. An optimal tuning rule to control the width of the kernel and the variance of the artificial noise added to the parameters is also proposed. The approach is illustrated through numerical examples.

Crowdsourcing is an effective tool for human-powered computation on many tasks challenging for computers. In this paper, we provide finite-sample exponential bounds on the error rate (in probability and in expectation) of hyperplane binary labeling rules under the Dawid-Skene crowdsourcing model. The bounds can be applied to analyze many common prediction methods, including the majority voting and weighted majority voting. These bound results could be useful for controlling the error rate and designing better algorithms. We show that the oracle Maximum A Posterior (MAP) rule approximately optimizes our upper bound on the mean error rate for any hyperplane binary labeling rule, and propose a simple data-driven weighted majority voting (WMV) rule (called one-step WMV) that attempts to approximate the oracle MAP and has a provable theoretical guarantee on the error rate. Moreover, we use simulated and real data to demonstrate that the data-driven EM-MAP rule is a good approximation to the oracle MAP rule, and to demonstrate that the mean error rate of the data-driven EM-MAP rule is also bounded by the mean error rate bound of the oracle MAP rule with estimated parameters plugging into the bound.

Intermittent fault localization approaches account for the fact that faulty components may fail intermittently by considering a parameter (known as goodness) that quantifies the probability that faulty components may still exhibit correct behavior. Current, state-of-the-art approaches (1) assume that this goodness probability is context independent and (2) do not provide means for integrating past diagnosis experience in the diagnostic mechanism. In this paper, we present a novel approach, coined Non-linear Feedback-based Goodness Estimate (NFGE), that uses kernel density estimations (KDE) to address such limitations. We evaluated the approach with both synthetic and real data, yielding lower estimation errors, thus increasing the diagnosis performance.

In spite of the significant work that has been done todiscover and recognize activities in the smart home re-search, less attention has been paid to predict the futureactivities that the resident is likely to perform. An ac-tivity prediction module can play a major role in designof a smart home. For instance, by taking advantage ofan activity prediction module, a smart home can learncontext-aware rules to prompt individuals to initiate im-portant activities. In this paper, we propose an activityprediction approach using Bayesian networks. We pro-pose a novel two-step inference process to predict thenext activity features and then to predict the next activ-ity label. We also propose an approach to predict thestart time of the next activity which is based on model-ing the relative start time of the predicted activity usinga continuous normal distribution and outlier detection.We evaluate our proposed models using real data col-lected from two smart home apartments.

Opponents are characterized by a Bayesian network intended to guide Monte-Carlo Tree Search through the game tree of No-Limit Texas Hold'em Poker. By using a probabilistic model of opponents, the network is able to integrate all available sources of information, including the infrequent revelations of hidden beliefs. These revelations are biased, and as such are difficult to incorporate into action prediction. The proposed network mitigates this bias via the expectation maximization algorithm and a probabilistic characterization of the hidden variables that generate observations. 

We propose here an approach for learning parameters in Bayesian networks from incomplete datasets that are subject to equivalence constraints. These equivalence constraints arise from datasets where examples are tied together, in that we may not know the value of a particular variable, but whatever that value is, we know it must be the same across different examples. We formalize the problem by defining the notion of a constrained dataset — a dataset with equivalence constraints — and a corresponding constrained likelihood that we seek to optimize. We derive an EM algorithm to estimate parameters from constrained datasets, which reduces to the vanilla EM algorithm when estimating parameters from traditional datasets. Finally, we evaluate our general approach in clustering problems from semi-supervised learning, showing that it is competitive with more specialized approaches.

Adverse and anomalous (A&A) events are a serious concern in medical robots. We describe a system that can rapidly detect such events and predict their occurrence. As part of this system, we describe simulation, data collection and user interface tools we build for a robot for small animal biopsies. The data we collect consists of both the hardware state of the robot and variables in the software controller. We use this data to train dynamic Bayesian network models of the joint hardware-software state-space dynamics of the robot. Our empirical evaluation shows that (i) our models can accurately model normal behavior of the robot, (ii) they can rapidly detect anomalous behavior once it starts, (iii) they can accurately predict a future A&A event within a time window of it starting and (iv) the use of additional software variables beyond the hardware state of the robot is important in being able to detect and predict certain kinds of events.

Recent years have witnessed the tremendous development of social media, which attracts a vast number of Internet users. The high-dimension content generated by these users provides an unique opportunity to understand their behavior deeply. As one of the most fundamental topics, location estimation attracts more and more research efforts. Different from the previous literature, we find that user's location is strongly related to user interest. Based on this, we first build a detection model to mine user interest from short text. We then establish the mapping between location function and user interest before presenting an efficient framework to predict the user's location with convincing fidelity. Thorough evaluations and comparisons on an authentic data set show that our proposed model significantly outperforms the state-of-the-arts approaches. Moreover, the high efficiency of our model also guarantees its applicability in real-world scenarios.

Mixed probabilistic and deterministic graphical models are ubiquitous in real-world applications. Unfortunately, Gibbs sampling, a popular MCMC technique, does not converge to the correct answers in presence of determinism and therefore cannot be used for inference in such models. In this paper, we propose to remedy this problem by combining Gibbs sampling with SampleSearch, an advanced importance sampling technique which leverages complete SAT/CSP solvers to generate high quality samples from hard deterministic spaces. We call the resulting algorithm, GiSS. Unlike Gibbs sampling which yields unweighted samples, GiSS yields weighted samples. Computing these weights exactly can be computationally expensive and therefore we propose several approximations. We show that our approximate weighting schemes yield consistent estimates and demonstrate experimentally that GiSS is competitive in terms of accuracy with state-of-the-art algorithms such as SampleSearch, MC-SAT and Belief propagation.