The compact Genetic Algorithm (cGA) is an Estimation of Distribution Algorithm that generates offspring population according to the estimated probabilistic model of the parent population instead of using traditional recombination and mutation operators. The cGA only needs a small amount of memory; therefore, it may be quite useful in memory-constrained applications. This paper introduces a theoretical framework for studying the cGA from the convergence point of view in which, we model the cGA by a Markov process and approximate its behavior using an Ordinary Differential Equation (ODE). Then, we prove that the corresponding ODE converges to local optima and stays there. Consequently, we conclude that the cGA will converge to the local optima of the function to be optimized.

Due to the dynamic nature of biological systems, biological networks underlying temporal process such as the development of {\it Drosophila melanogaster} can exhibit significant topological changes to facilitate dynamic regulatory functions. Thus it is essential to develop methodologies that capture the temporal evolution of networks, which make it possible to study the driving forces underlying dynamic rewiring of gene regulation circuity, and to predict future network structures. Using a new machine learning method called Tesla, which builds on a novel temporal logistic regression technique, we report the first successful genome-wide reverse-engineering of the latent sequence of temporally rewiring gene networks over more than 4000 genes during the life cycle of \textit{Drosophila melanogaster}, given longitudinal gene expression measurements and even when a single snapshot of such measurement resulted from each (time-specific) network is available. Our methods offer the first glimpse of time-specific snapshots and temporal evolution patterns of gene networks in a living organism during its full developmental course. The recovered networks with this unprecedented resolution chart the onset and duration of many gene interactions which are missed by typical static network analysis, and are suggestive of a wide array of other temporal behaviors of the gene network over time not noticed before.

We unify f-divergences, Bregman divergences, surrogate loss bounds (regret bounds), proper scoring rules, matching losses, cost curves, ROC-curves and information. We do this by systematically studying integral and variational representations of these objects and in so doing identify their primitives which all are related to cost-sensitive binary classification. As well as clarifying relationships between generative and discriminative views of learning, the new machinery leads to tight and more general surrogate loss bounds and generalised Pinsker inequalities relating f-divergences to variational divergence. The new viewpoint illuminates existing algorithms: it provides a new derivation of Support Vector Machines in terms of divergences and relates Maximum Mean Discrepancy to Fisher Linear Discriminants. It also suggests new techniques for estimating f-divergences.

Artificial Chemistries (ACs) are symbolic chemical metaphors for the exploration of Artificial Life, with specific focus on the problem of biogenesis or the origin of life. This paper presents authors thoughts towards defining a unified framework to characterize and classify symbolic artificial chemistries by devising appropriate formalism to capture semantic and organizational information. We identify three basic high level abstractions in initial proposal for this framework viz., information, computation, and communication. We present an analysis of two important notions of information, namely, Shannon's Entropy and Algorithmic Information, and discuss inductive and deductive approaches for defining the framework.

Artificial Chemistries (ACs) are symbolic chemical metaphors for the exploration of Artificial Life, with specific focus on the origin of life. In this work we define a P system based artificial graph chemistry to understand the principles leading to the evolution of life-like structures in an AC set up and to develop a unified framework to characterize and classify symbolic artificial chemistries by devising appropriate formalism to capture semantic and organizational information. An extension of P system is considered by associating probabilities with the rules providing the topological framework for the evolution of a labeled undirected graph based molecular reaction semantics.

Semantic memory refers to our knowledge of facts and relationships between concepts. Asuccessful semantic memory depends on inferring relationships between items that are not explicitly taught. Recent mathematical modeling of episodic memory argues that episodic recall relies on retrieval of a gradually-changing representation oftemporal context. We show that retrieved context enables the development of a global memory space that reflects relationships between all items that have been previously learned. When newly-learned information is integrated into this structure, it is placed in some relationship to all other items, even if that relationship has not been explicitly learned. We demonstrate this effect for global semantic structures shaped topologically as a ring, and as a two-dimensional sheet. We also examined the utility of this learning algorithm for learning a more realistic semantic space by training it on a large pool of synonym pairs. Retrieved context enabled the model to "infer" relationships between synonym pairs that had not yet been presented.

We extend the Bayesian skill rating system TrueSkill to infer entire time series of skills of players by smoothing through time instead of filtering. The skill of each participating player, say, every year is represented by a latent skill variable which is affected by the relevant game outcomes that year, and coupled with the skill variables of the previous and subsequent year. Inference in the resulting factor graph is carried out by approximate message passing (EP) along the time series of skills. As before the system tracks the uncertainty about player skills, explicitly models draws, can deal with any number of competing entities and can infer individual skills from team results. We extend the system to estimate player-specific draw margins. Basedon these models we present an analysis of the skill curves of important players in the history of chess over the past 150 years. Results include plots of players' lifetime skill development as well as the ability to compare the skills of different players across time. Our results indicate that a) the overall playing strength has increased over the past 150 years, and b) that modelling a player's ability to force a draw provides significantly better predictive power.

We present a theoretical study on the discriminative clustering framework, recently proposed for simultaneous subspace selection via linear discriminant analysis (LDA) and clustering. Empirical results have shown its favorable performance in comparison with several other popular clustering algorithms. However, the inherent relationship between subspace selection and clustering in this framework is not well understood, due to the iterative nature of the algorithm. We show in this paper that this iterative subspace selection and clustering is equivalent to kernel K-means with a specific kernel Gram matrix. This provides significant and new insights into the nature of this subspace selection procedure. Based on this equivalence relationship, we propose the Discriminative K-means (DisKmeans) algorithm for simultaneous LDA subspace selection and clustering, as well as an automatic parameter estimation procedure. We also present the nonlinear extension of DisKmeans using kernels. We show that the learning of the kernel matrix over a convex set of pre-specified kernel matrices can be incorporated into the clustering formulation. The connection between DisKmeans and several other clustering algorithms is also analyzed. The presented theories and algorithms are evaluated through experiments on a collection of benchmark data sets.

In problems where input features have varying amounts of noise, using distinct regularization hyperparameters for different features provides an effective means of managing model complexity. While regularizers for neural networks and support vectormachines often rely on multiple hyperparameters, regularizers for structured prediction models (used in tasks such as sequence labeling or parsing) typicallyrely only on a single shared hyperparameter for all features. In this paper, we consider the problem of choosing regularization hyperparameters for log-linear models, a class of structured prediction probabilistic models which includes conditionalrandom fields (CRFs). Using an implicit differentiation trick, we derive an efficient gradient-based method for learning Gaussian regularization priors with multiple hyperparameters. In both simulations and the real-world task of computational RNA secondary structure prediction, we find that multiple hyperparameter learningcan provide a significant boost in accuracy compared to using only a single regularization hyperparameter.

We present sharp rates of convergence (with respect to additive regret) for both the full information setting (where the cost function is revealed at the end of each round) and the bandit setting (where only the scalar cost incurred is revealed). In particular, this paper is concerned with the price of bandit information, by which we mean the ratio of the best achievable regret in the bandit setting to that in the full-information setting.