Linear-time computational techniques have been developed for combining evidence which is available on a number of contending hypotheses. They offer a means of making the computation-intensive calculations involved more efficient in certain circumstances. Unfortunately, they restrict the orthogonal sum of evidential functions to the dichotomous structure applies only to elements and their complements. In this paper, we present a novel evidence structure in terms of a triplet and a set of algorithms for evidential reasoning. The merit of this structure is that it divides a set of evidence into three subsets, distinguishing trivial evidential elements from important ones focusing some particular elements. It avoids the deficits of the dichotomous structure in representing the preference of evidence and estimating the basic probability assignment of evidence. We have established a formalism for this structure and the general formulae for combining pieces of evidence in the form of the triplet, which have been theoretically justified.

This paper studies a new and more general axiomatization than one presented previously for preference on likelihood gambles. Likelihood gambles describe actions in a situation where a decision maker knows multiple probabilistic models and a random sample generated from one of those models but does not know prior probability of models. This new axiom system is inspired by Jensen's axiomatization of probabilistic gambles. Our approach provides a new perspective to the role of data in decision making under ambiguity. It avoids one of the most controversial issue of Bayesian methodology namely the assumption of prior probability.

We consider the problem of learning the optimal action-value function in the discounted-reward Markov decision processes (MDPs). We prove a new PAC bound on the sample-complexity of model-based value iteration algorithm in the presence of the generative model, which indicates that for an MDP with N state-action pairs and the discount factor \gamma\in[0,1) only O(N\log(N/\delta)/((1-\gamma)^3\epsilon^2)) samples are required to find an \epsilon-optimal estimation of the action-value function with the probability 1-\delta. We also prove a matching lower bound of \Theta (N\log(N/\delta)/((1-\gamma)^3\epsilon^2)) on the sample complexity of estimating the optimal action-value function by every RL algorithm. To the best of our knowledge, this is the first matching result on the sample complexity of estimating the optimal (action-) value function in which the upper bound matches the lower bound of RL in terms of N, \epsilon, \delta and 1/(1-\gamma). Also, both our lower bound and our upper bound significantly improve on the state-of-the-art in terms of 1/(1-\gamma).

We consider the problem of learning object arrangements in a 3D scene. The key idea here is to learn how objects relate to human poses based on their affordances, ease of use and reachability. In contrast to modeling object-object relationships, modeling human-object relationships scales linearly in the number of objects. We design appropriate density functions based on 3D spatial features to capture this. We learn the distribution of human poses in a scene using a variant of the Dirichlet process mixture model that allows sharing of the density function parameters across the same object types. Then we can reason about arrangements of the objects in the room based on these meaningful human poses. In our extensive experiments on 20 different rooms with a total of 47 objects, our algorithm predicted correct placements with an average error of 1.6 meters from ground truth. In arranging five real scenes, it received a score of 4.3/5 compared to 3.7 for the best baseline method.

The effect of inaccuracies in the parameters of a dynamic Bayesian network can be investigated by subjecting the network to a sensitivity analysis. Having detailed the resulting sensitivity functions in our previous work, we now study the effect of parameter inaccuracies on a recommended decision in view of a threshold decision-making model. We detail the effect of varying a single and multiple parameters from a conditional probability table and present a computational procedure for establishing bounds between which assessments for these parameters can be varied without inducing a change in the recommended decision. We illustrate the various concepts involved by means of a real-life dynamic network in the field of infectious disease.

As machine learning algorithms enter applications in industrial settings, there is increased interest in controlling their cpu-time during testing. The cpu-time consists of the running time of the algorithm and the extraction time of the features. The latter can vary drastically when the feature set is diverse. In this paper, we propose an algorithm, the Greedy Miser, that incorporates the feature extraction cost during training to explicitly minimize the cpu-time during testing. The algorithm is a straightforward extension of stage-wise regression and is equally suitable for regression or multi-class classification. Compared to prior work, it is significantly more cost-effective and scales to larger data sets.

We consider analysis of relational data (a matrix), in which the rows correspond to subjects (e.g., people) and the columns correspond to attributes. The elements of the matrix may be a mix of real and categorical. Each subject and attribute is characterized by a latent binary feature vector, and an inferred matrix maps each row-column pair of binary feature vectors to an observed matrix element. The latent binary features of the rows are modeled via a multivariate Gaussian distribution with low-rank covariance matrix, and the Gaussian random variables are mapped to latent binary features via a probit link. The same type construction is applied jointly to the columns. The model infers latent, low-dimensional binary features associated with each row and each column, as well correlation structure between all rows and between all columns.

We investigate the problem of modeling symbolic sequences of polyphonic music in a completely general piano-roll representation. We introduce a probabilistic model based on distribution estimators conditioned on a recurrent neural network that is able to discover temporal dependencies in high-dimensional sequences. Our approach outperforms many traditional models of polyphonic music on a variety of realistic datasets. We show how our musical language model can serve as a symbolic prior to improve the accuracy of polyphonic transcription.

Online learning algorithms are designed to learn even when their input is generated by an adversary. The widely-accepted formal definition of an online algorithm's ability to learn is the game-theoretic notion of regret. We argue that the standard definition of regret becomes inadequate if the adversary is allowed to adapt to the online algorithm's actions. We define the alternative notion of policy regret, which attempts to provide a more meaningful way to measure an online algorithm's performance against adaptive adversaries. Focusing on the online bandit setting, we show that no bandit algorithm can guarantee a sublinear policy regret against an adaptive adversary with unbounded memory. On the other hand, if the adversary's memory is bounded, we present a general technique that converts any bandit algorithm with a sublinear regret bound into an algorithm with a sublinear policy regret bound. We extend this result to other variants of regret, such as switching regret, internal regret, and swap regret.

In this paper we provide a principled approach to solve a transductive classification problem involving a similar graph (edges tend to connect nodes with same labels) and a dissimilar graph (edges tend to connect nodes with opposing labels). Most of the existing methods, e.g., Information Regularization (IR), Weighted vote Relational Neighbor classifier (WvRN) etc, assume that the given graph is only a similar graph. We extend the IR and WvRN methods to deal with mixed graphs. We evaluate the proposed extensions on several benchmark datasets as well as two real world datasets and demonstrate the usefulness of our ideas.