Flower pollination algorithm is a recent metaheuristic algorithm for solving nonlinear global optimization problems. The algorithm has also been extended to solve multiobjective optimization with promising results. In this work, we analyze this algorithm mathematically and prove its convergence properties by using Markov chain theory. By constructing the appropriate transition probability for a population of flower pollen and using the homogeneity property, it can be shown that the constructed stochastic sequences can converge to the optimal set. Under the two proper conditions for convergence, it is proved that the simplified flower pollination algorithm can indeed satisfy these convergence conditions and thus the global convergence of this algorithm can be guaranteed. Numerical experiments are used to demonstrate that the flower pollination algorithm can converge quickly in practice and can thus achieve global optimality efficiently.

The Synthetic Minority Oversampling Technique (SMOTE) preprocessing algorithm is considered "de facto" standard in the framework of learning from imbalanced data. This is due to its simplicity in the design of the procedure, as well as its robustness when applied to different type of problems. Since its publication in 2002, SMOTE has proven successful in a variety of applications from several different domains. SMOTE has also inspired several approaches to counter the issue of class imbalance, and has also significantly contributed to new supervised learning paradigms, including multilabel classification, incremental learning, semi-supervised learning, multi-instance learning, among others. It is standard benchmark for learning from imbalanced data. It is also featured in a number of different software packages -- from open source to commercial. In this paper, marking the fifteen year anniversary of SMOTE, we reflect on the SMOTE journey, discuss the current state of affairs with SMOTE, its applications, and also identify the next set of challenges to extend SMOTE for Big Data problems.

We show that the visible sector probability density function of the Riemann-Theta Boltzmann machine corresponds to a gaussian mixture model consisting of an infinite number of component multi-variate gaussians. The weights of the mixture are given by a discrete multi-variate gaussian over the hidden state space. This allows us to sample the visible sector density function in a straight-forward manner. Furthermore, we show that the visible sector probability density function possesses an affine transform property, similar to the multi-variate gaussian density.

Gibbs sampling, as a model learning method, is known to produce the most accurate results available in a variety of domains, and is a de facto standard in these domains. Yet, it is also well known that Gibbs random walks usually have bottlenecks, sometimes termed "local maxima", and thus samplers often return suboptimal solutions. In this paper we introduce a variation of the Gibbs sampler which yields high likelihood solutions significantly more often than the regular Gibbs sampler. Specifically, we show that combining multiple samplers, with certain dependence (coupling) between them, results in higher likelihood solutions. This side-steps the well known issue of identifiability, which has been the obstacle to combining samplers in previous work. We evaluate the approach on a Latent Dirichlet Allocation model, and also on HMM's, where precise computation of likelihoods and comparisons to the standard EM algorithm are possible.

We consider planning problems for graphs, Markov decision processes (MDPs), and games on graphs. While graphs represent the most basic planning model, MDPs represent interaction with nature and games on graphs represent interaction with an adversarial environment. We consider two planning problems where there are k different target sets, and the problems are as follows: (a) the coverage problem asks whether there is a plan for each individual target set; and (b) the sequential target reachability problem asks whether the targets can be reached in sequence. For the coverage problem, we present a linear-time algorithm for graphs, and quadratic conditional lower bound for MDPs and games on graphs. For the sequential target problem, we present a linear-time algorithm for graphs, a sub-quadratic algorithm for MDPs, and a quadratic conditional lower bound for games on graphs. Our results with conditional lower bounds establish (i) modelseparation results showing that for the coverage problem MDPs and games on graphs are harder than graphs, and for the sequential reachability problem games on graphs are harder than MDPs and graphs; and (ii) objective-separation results showing that for MDPs the coverage problem is harder than the sequential target problem.

This thesis investigates unsupervised time series representation learning for sequence prediction problems, i.e. generating nice-looking input samples given a previous history, for high dimensional input sequences by decoupling the static input representation from the recurrent sequence representation. We introduce three models based on Generative Stochastic Networks (GSN) for unsupervised sequence learning and prediction. Experimental results for these three models are presented on pixels of sequential handwritten digit (MNIST) data, videos of low-resolution bouncing balls, and motion capture data. The main contribution of this thesis is to provide evidence that GSNs are a viable framework to learn useful representations of complex sequential input data, and to suggest a new framework for deep generative models to learn complex sequences by decoupling static input representations from dynamic time dependency representations.

This paper addresses the problem of planning a safe (i.e., collision-free) trajectory from an initial state to a goal region when the obstacle space is a-priori unknown and is incrementally revealed online, e.g., through line-of-sight perception. Despite its ubiquitous nature, this formulation of motion planning has received relatively little theoretical investigation, as opposed to the setup where the environment is assumed known. A fundamental challenge is that, unlike motion planning with known obstacles, it is not even clear what an optimal policy to strive for is. Our contribution is threefold. First, we present a notion of optimality for safe planning in unknown environments in the spirit of comparative (as opposed to competitive) analysis, with the goal of obtaining a benchmark that is, at least conceptually, attainable. Second, by leveraging this theoretical benchmark, we derive a pseudo-optimal class of policies that can seamlessly incorporate any amount of prior or learned information while still guaranteeing the robot never collides. Finally, we demonstrate the practicality of our algorithmic approach in numerical experiments using a range of environment types and dynamics, including a comparison with a state of the art method. A key aspect of our framework is that it automatically and implicitly weighs exploration versus exploitation in a way that is optimal with respect to the information available.

With a new era of cloud and big data, Database Management Systems (DBMSs) have become more crucial in numerous enterprise business applications in all the industries. Accordingly, the importance of their proactive and preventive maintenance has also increased. However, detecting problems by predefined rules or stochastic modeling has limitations, particularly when analyzing the data on high-dimensional Key Performance Indicators (KPIs) from a DBMS. In recent years, Deep Learning (DL) has opened new opportunities for this complex analysis. In this paper, we present two complementary DL approaches to detect anomalies in SAP HANA. A temporal learning approach is used to detect abnormal patterns based on unlabeled historical data, whereas a spatial learning approach is used to classify known anomalies based on labeled data. We implement a system in SAP HANA integrated with Google TensorFlow. The experimental results with real-world data confirm the effectiveness of the system and models.

This paper considers parametric Markov decision processes (pMDPs) whose transitions are equipped with affine functions over a finite set of parameters. The synthesis problem is to find a parameter valuation such that the instantiated pMDP satisfies a specification under all strategies. We show that this problem can be formulated as a quadratically-constrained quadratic program (QCQP) and is non-convex in general. To deal with the NP-hardness of such problems, we exploit a convex-concave procedure (CCP) to iteratively obtain local optima. An appropriate interplay between CCP solvers and probabilistic model checkers creates a procedure --- realized in the open-source tool PROPhESY --- that solves the synthesis problem for models with thousands of parameters.

Natural Language Generation is a very important area to be explored in our time. It forms the basis of how a bot would communicate with -- not like how literates write books but like how we talk. In this Kernel, I'd like to show you a very simple but powerful Python module that does a similar exercise in (literally) a couple of lines of code. The Py module we use here is markovify. Markovify is a simple, extensible Markov chain generator.