Density mode clustering is a nonparametric clustering method. The clusters are the basins of attraction of the modes of a density estimator. We study the risk of mode-based clustering. We show that the clustering risk over the cluster cores --- the regions where the density is high --- is very small even in high dimensions. And under a low noise condition, the overall cluster risk is small even beyond the cores, in high dimensions.

In biospectroscopy, suitably annotated and statistically independent samples (e. g. patients, batches, etc.) for classifier training and testing are scarce and costly. Learning curves show the model performance as function of the training sample size and can help to determine the sample size needed to train good classifiers. However, building a good model is actually not enough: the performance must also be proven. We discuss learning curves for typical small sample size situations with 5 - 25 independent samples per class. Although the classification models achieve acceptable performance, the learning curve can be completely masked by the random testing uncertainty due to the equally limited test sample size. In consequence, we determine test sample sizes necessary to achieve reasonable precision in the validation and find that 75 - 100 samples will usually be needed to test a good but not perfect classifier. Such a data set will then allow refined sample size planning on the basis of the achieved performance. We also demonstrate how to calculate necessary sample sizes in order to show the superiority of one classifier over another: this often requires hundreds of statistically independent test samples or is even theoretically impossible. We demonstrate our findings with a data set of ca. 2550 Raman spectra of single cells (five classes: erythrocytes, leukocytes and three tumour cell lines BT-20, MCF-7 and OCI-AML3) as well as by an extensive simulation that allows precise determination of the actual performance of the models in question.

Automatic classification of scientific articles based on common characteristics is an interesting problem with many applications in digital library and information retrieval systems. Properly organized articles can be useful for automatic generation of taxonomies in scientific writings, textual summarization, efficient information retrieval etc. Generating article bundles from a large number of input articles, based on the associated features of the articles is tedious and computationally expensive task. In this report we propose an automatic two-step approach for topic extraction and bundling of related articles from a set of scientific articles in real-time. For topic extraction, we make use of Latent Dirichlet Allocation (LDA) topic modeling techniques and for bundling, we make use of hierarchical agglomerative clustering techniques. We run experiments to validate our bundling semantics and compare it with existing models in use. We make use of an online crowdsourcing marketplace provided by Amazon called Amazon Mechanical Turk to carry out experiments. We explain our experimental setup and empirical results in detail and show that our method is advantageous over existing ones.

Particle Swarm Optimization (PSO) is a nature-inspired meta-heuristic for solving continuous optimization problems. In the literature, the potential of the particles of swarm has been used to show that slightly modified PSO guarantees convergence to local optima. Here we show that under specific circumstances the unmodified PSO, even with swarm parameters known (from the literature) to be good, almost surely does not yield convergence to a local optimum is provided. This undesirable phenomenon is called stagnation. For this purpose, the particles' potential in each dimension is analyzed mathematically. Additionally, some reasonable assumptions on the behavior if the particles' potential are made. Depending on the objective function and, interestingly, the number of particles, the potential in some dimensions may decrease much faster than in other dimensions. Therefore, these dimensions lose relevance, i.e., the contribution of their entries to the decisions about attractor updates becomes insignificant and, with positive probability, they never regain relevance. If Brownian Motion is assumed to be an approximation of the time-dependent drop of potential, practical, i.e., large values for this probability are calculated. Finally, on chosen multidimensional polynomials of degree two, experiments are provided showing that the required circumstances occur quite frequently. Furthermore, experiments are provided showing that even when the very simple sphere function is processed the described stagnation phenomenon occurs. Consequently, unmodified PSO does not converge to any local optimum of the chosen functions for tested parameter settings.

Tapani Raiko Aalto University, Finland We show how a deep denoising autoencoder with lateral connections can be used as an auxiliary unsupervised learning task to support supervised learning. The proposed model is trained to minimize simultaneously the sum of supervised and unsupervised cost functions by back-propagation, avoiding the need for layerwise pretraining. It improves the state of the art significantly in the permutationinvariant MNIST classification task.

Multi-context Systems (MCSs) are a formalism for systems consisting of knowledge bases (possibly heterogeneous and non-monotonic) that are interlinked via bridge rules, where the global system semantics emerges from the local semantics of the knowledge bases (also called contexts) in an equilibrium. While MCSs and related formalisms are inherently targeted for distributed set- tings, no truly distributed algorithms for their evaluation were available. We address this short- coming and present a suite of such algorithms which includes a basic algorithm DMCS, an ad- vanced version DMCSOPT that exploits topology-based optimizations, and a streaming algorithm DMCS-STREAMING that computes equilibria in packages of bounded size. The algorithms be- have quite differently in several respects, as experienced in thorough experimental evaluation of a system prototype. From the experimental results, we derive a guideline for choosing the appropriate algorithm and running mode in particular situations, determined by the parameter settings.

We introduce an approximate search algorithm for fast maximum a posteriori probability estimation in probabilistic programs, which we call Bayesian ascent Monte Carlo (BaMC). Probabilistic programs represent probabilistic models with varying number of mutually dependent finite, countable, and continuous random variables. BaMC is an anytime MAP search algorithm applicable to any combination of random variables and dependencies. We compare BaMC to other MAP estimation algorithms and show that BaMC is faster and more robust on a range of probabilistic models.

In this paper we introduce a novel method for linear system identification with quantized output data. We model the impulse response as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. This serves as a starting point to cast our system identification problem into a Bayesian framework. We employ Markov Chain Monte Carlo (MCMC) methods to provide an estimate of the system. In particular, we show how to design a Gibbs sampler which quickly converges to the target distribution. Numerical simulations show a substantial improvement in the accuracy of the estimates over state-of-the-art kernel-based methods when employed in identification of systems with quantized data.1. INTRODUCTION Identification of systems from quantized data finds applications in a wide range of areas such as communications, networked control systems, bioinformatics (see e.g.

Bayesian probability theory is one of the most successful frameworks to model reasoning under uncertainty. Its defining property is the interpretation of probabilities as degrees of belief in propositions about the state of the world relative to an inquiring subject. This essay examines the notion of subjectivity by drawing parallels between Lacanian theory and Bayesian probability theory, and concludes that the latter must be enriched with causal interventions to model agency. The central contribution of this work is an abstract model of the subject that accommodates causal interventions in a measure-theoretic formalisation. This formalisation is obtained through a game-theoretic Ansatz based on modelling the inside and outside of the subject as an extensive-form game with imperfect information between two players. Finally, I illustrate the expressiveness of this model with an example of causal induction.

Within the natural language processing (NLP) community, active learning has been widely investigated and applied in order to alleviate the annotation bottleneck faced by developers of new NLP systems and technologies. This paper presents the first theoretical analysis of stopping active learning based on stabilizing predictions (SP). The analysis has revealed three elements that are central to the success of the SP method: (1) bounds on Cohen's Kappa agreement between successively trained models impose bounds on differences in F-measure performance of the models; (2) since the stop set does not have to be labeled, it can be made large in practice, helping to guarantee that the results transfer to previously unseen streams of examples at test/application time; and (3) good (low variance) sample estimates of Kappa between successive models can be obtained. Proofs of relationships between the level of Kappa agreement and the difference in performance between consecutive models are presented. Specifically, if the Kappa agreement between two models exceeds a threshold T (where $T>0$), then the difference in F-measure performance between those models is bounded above by $\frac{4(1-T)}{T}$ in all cases. If precision of the positive conjunction of the models is assumed to be $p$, then the bound can be tightened to $\frac{4(1-T)}{(p+1)T}$.