We introduce and develop a novel approach to outlier detection based on adaptation of random subspace learning. Our proposed method handles both high-dimension low-sample size and traditional low-dimensional high-sample size datasets. Essentially, we avoid the computational bottleneck of techniques like minimum covariance determinant (MCD) by computing the needed determinants and associated measures in much lower dimensional subspaces. Both theoretical and computational development of our approach reveal that it is computationally more efficient than the regularized methods in high-dimensional low-sample size, and often competes favorably with existing methods as far as the percentage of correct outlier detection is concerned.

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.

We present the multiplicative recurrent neural network as a general model for compositional meaning in language, and evaluate it on the task of fine-grained sentiment analysis. We establish a connection to the previously investigated matrix-space models for compositionality, and show they are special cases of the multiplicative recurrent net. Our experiments show that these models perform comparably or better than Elman-type additive recurrent neural networks and outperform matrix-space models on a standard fine-grained sentiment analysis corpus. Furthermore, they yield comparable results to structural deep models on the recently published Stanford Sentiment Treebank without the need for generating parse trees.

NMF suffers from the scale and ordering ambiguities. Often, the source signals can be monotonous in nature. For example, in source separation problem, the source signals can be monotonously increasing or decreasing while the mixing matrix can have nonnegative entries. NMF methods may not be effective for such cases as it suffers from the ordering ambiguity. This paper proposes an approach to incorporate notion of monotonicity in NMF, labeled as monotonous NMF. An algorithm based on alternating least-squares is proposed for recovering monotonous signals from a data matrix. Further, the assumption on mixing matrix is relaxed to extend monotonous NMF for data matrix with real numbers as entries. The approach is illustrated using synthetic noisy data. The results obtained by monotonous NMF are compared with standard NMF algorithms in the literature, and it is shown that monotonous NMF estimates source signals well in comparison to standard NMF algorithms when the underlying sources signals are monotonous.

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.

Learning in restricted Boltzmann machine is typically hard due to the computation of gradients of log-likelihood function. To describe the network state statistics of the restricted Boltzmann machine, we develop an advanced mean field theory based on the Bethe approximation. Our theory provides an efficient message passing based method that evaluates not only the partition function (free energy) but also its gradients without requiring statistical sampling. The results are compared with those obtained by the computationally expensive sampling based method.

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.

We present an approach to simultaneously reasoning about a video clip and an entire natural-language sentence. The compositional nature of language is exploited to construct models which represent the meanings of entire sentences composed out of the meanings of the words in those sentences mediated by a grammar that encodes the predicate-argument relations. We demonstrate that these models faithfully represent the meanings of sentences and are sensitive to how the roles played by participants (nouns), their characteristics (adjectives), the actions performed (verbs), the manner of such actions (adverbs), and changing spatial relations between participants (prepositions) affect the meaning of a sentence and how it is grounded in video. We exploit this methodology in three ways. In the first, a video clip along with a sentence are taken as input and the participants in the event described by the sentence are highlighted, even when the clip depicts multiple similar simultaneous events. In the second, a video clip is taken as input without a sentence and a sentence is generated that describes an event in that clip. In the third, a corpus of video clips is paired with sentences which describe some of the events in those clips and the meanings of the words in those sentences are learned. We learn these meanings without needing to specify which attribute of the video clips each word in a given sentence refers to. The learned meaning representations are shown to be intelligible to humans.

This article considers the problem of sparse estimation of canonical vectors in linear discriminant analysis when $p\gg N$. Several methods have been proposed in the literature that estimate one canonical vector in the two-group case. However, $G-1$ canonical vectors can be considered if the number of groups is $G$. In the multi-group context, it is common to estimate canonical vectors in a sequential fashion. Moreover, separate prior estimation of the covariance structure is often required. We propose a novel methodology for direct estimation of canonical vectors. In contrast to existing techniques, the proposed method estimates all canonical vectors at once, performs variable selection across all the vectors and comes with theoretical guarantees on the variable selection and classification consistency. First, we highlight the fact that in the $N>p$ setting the canonical vectors can be expressed in a closed form up to an orthogonal transformation. Secondly, we propose an extension of this form to the $p\gg N$ setting and achieve feature selection by using a group penalty. The resulting optimization problem is convex and can be solved using a block-coordinate descent algorithm. The practical performance of the method is evaluated through simulation studies as well as real data applications.

In Constraint Programming (CP), a portfolio solver uses a variety of different solvers for solving a given Constraint Satisfaction / Optimization Problem. In this paper we introduce sunny-cp2: the first parallel CP portfolio solver that enables a dynamic, cooperative, and simultaneous execution of its solvers in a multicore setting. It incorporates state-of-the-art solvers, providing also a usable and configurable framework. Empirical results are very promising.