Kernel Induced Random Survival Forests (KIRSF) is a statistical learning algorithm which aims to improve prediction accuracy for survival data. As in Random Survival Forests (RSF), Cumulative Hazard Function is predicted for each individual in the test set. Prediction error is estimated using Harrell's concordance index (C index) [Harrell et al. (1982)]. The C-index can be interpreted as a misclassification probability and does not depend on a single fixed time for evaluation. The C-index also specifically accounts for censoring. By utilizing kernel functions, KIRSF achieves better results than RSF in many situations. In this report, we show how to incorporate kernel functions into RSF. We test the performance of KIRSF and compare our method to RSF. We find that the KIRSF's performance is better than RSF in many occasions.

We provide a series of algorithms demonstrating that solutions according to the fundamental game-theoretic solution concept of closed under rational behavior (CURB) sets in two-player, normal-form games can be computed in polynomial time (we also discuss extensions to n-player games). First, we describe an algorithm that identifies all of a players best responses conditioned on the belief that the other player will play from within a given subset of its strategy space. This algorithm serves as a subroutine in a series of polynomial-time algorithms for finding all minimal CURB sets, one minimal CURB set, and the smallest minimal CURB set in a game. We then show that the complexity of finding a Nash equilibrium can be exponential only in the size of a games smallest CURB set. Related to this, we show that the smallest CURB set can be an arbitrarily small portion of the game, but it can also be arbitrarily larger than the supports of its only enclosed Nash equilibrium. We test our algorithms empirically and find that most commonly studied academic games tend to have either very large or very small minimal CURB sets.

In the last few years, many different performance measures have been introduced to overcome the weakness of the most natural metric, the Accuracy. Among them, Matthews Correlation Coefficient has recently gained popularity among researchers not only in machine learning but also in several application fields such as bioinformatics. Nonetheless, further novel functions are being proposed in literature. We show that Confusion Entropy, a recently introduced classifier performance measure for multi-class problems, has a strong (monotone) relation with the multi-class generalization of a classical metric, the Matthews Correlation Coefficient. Computational evidence in support of the claim is provided, together with an outline of the theoretical explanation.

This paper proposes a method to construct an adaptive agent that is universal with respect to a given class of experts, where each expert is designed specifically for a particular environment. This adaptive control problem is formalized as the problem of minimizing the relative entropy of the adaptive agent from the expert that is most suitable for the unknown environment. If the agent is a passive observer, then the optimal solution is the well-known Bayesian predictor. However, if the agent is active, then its past actions need to be treated as causal interventions on the I/O stream rather than normal probability conditions. Here it is shown that the solution to this new variational problem is given by a stochastic controller called the Bayesian control rule, which implements adaptive behavior as a mixture of experts. Furthermore, it is shown that under mild assumptions, the Bayesian control rule converges to the control law of the most suitable expert.

We extend the mixtures of Gaussians (MOG) model to the projected mixture of Gaussians (PMOG) model. In the PMOG model, we assume that q dimensional input data points z_i are projected by a q dimensional vector w into 1-D variables u_i. The projected variables u_i are assumed to follow a 1-D MOG model. In the PMOG model, we maximize the likelihood of observing u_i to find both the model parameters for the 1-D MOG as well as the projection vector w. First, we derive an EM algorithm for estimating the PMOG model. Next, we show how the PMOG model can be applied to the problem of blind source separation (BSS). In contrast to conventional BSS where an objective function based on an approximation to differential entropy is minimized, PMOG based BSS simply minimizes the differential entropy of projected sources by fitting a flexible MOG model in the projected 1-D space while simultaneously optimizing the projection vector w. The advantage of PMOG over conventional BSS algorithms is the more flexible fitting of non-Gaussian source densities without assuming near-Gaussianity (as in conventional BSS) and still retaining computational feasibility.

Many problems of low-level computer vision and image processing, such as denoising, deconvolution, tomographic reconstruction or super-resolution, can be addressed by maximizing the posterior distribution of a sparse linear model (SLM). We show how higher-order Bayesian decision-making problems, such as optimizing image acquisition in magnetic resonance scanners, can be addressed by querying the SLM posterior covariance, unrelated to the density's mode. We propose a scalable algorithmic framework, with which SLM posteriors over full, high-resolution images can be approximated for the first time, solving a variational optimization problem which is convex iff posterior mode finding is convex. These methods successfully drive the optimization of sampling trajectories for real-world magnetic resonance imaging through Bayesian experimental design, which has not been attempted before. Our methodology provides new insight into similarities and differences between sparse reconstruction and approximate Bayesian inference, and has important implications for compressive sensing of real-world images.

This paper proposes a nonparametric Bayesian method for exploratory data analysis and feature construction in continuous time series. Our method focuses on understanding shared features in a set of time series that exhibit significant individual variability. Our method builds on the framework of latent Diricihlet allocation (LDA) and its extension to hierarchical Dirichlet processes, which allows us to characterize each series as switching between latent ``topics'', where each topic is characterized as a distribution over ``words'' that specify the series dynamics. However, unlike standard applications of LDA, we discover the words as we learn the model. We apply this model to the task of tracking the physiological signals of premature infants; our model obtains clinically significant insights as well as useful features for supervised learning tasks.

Markov models are extensively used in the analysis of molecular evolution. A recent line of research suggests that pairs of proteins with functional and physical interactions co-evolve with each other. Here, by analyzing hundreds of orthologous sets of three fungi and their co-evolutionary relations, we demonstrate that co-evolutionary assumption may violate the Markov assumption. Our results encourage developing alternative probabilistic models for the cases of extreme co-evolution. Markov models have been extensively used in studies and modeling of molecular evolution (see, for example, [1-11]).

Because an agent's resources dictate what actions it can possibly take, it should plan which resources it holds over time carefully, considering its inherent limitations (such as power or payload restrictions), the competing needs of other agents for the same resources, and the stochastic nature of the environment. Such agents can, in general, achieve more of their objectives if they can use -- and even create -- opportunities to change which resources they hold at various times. Driven by resource constraints, the agents could break their overall missions into an optimal series of phases, optimally reconfiguring their resources at each phase, and optimally using their assigned resources in each phase, given their knowledge of the stochastic environment. In this paper, we formally define and analyze this constrained, sequential optimization problem in both the single-agent and multi-agent contexts. We present a family of mixed integer linear programming (MILP) formulations of this problem that can optimally create phases(when phases are not predefined) accounting for costs and limitations in phase creation. Because our formulations simultaneously also find the optimal allocations of resources at each phase and the optimal policies for using the allocated resources at each phase, they exploit structure across these coupled problems. This allows them to find solutions significantly faster (orders of magnitude faster in larger problems) than alternative solution techniques, as we demonstrate empirically.

A Hidden Markov Model (HMM) is a common statistical model which is widely used for analysis of biological sequence data and other sequential phenomena. In the present paper we show how HMMs can be extended with side-constraints and present constraint solving techniques for efficient inference. Defining HMMs with side-constraints in Constraint Logic Programming have advantages in terms of more compact expression and pruning opportunities during inference. We present a PRISM-based framework for extending HMMs with side-constraints and show how well-known constraints such as cardinality and all different are integrated. We experimentally validate our approach on the biologically motivated problem of global pairwise alignment.