Model Selection Criteria for Segmented Time Series from a Bayesian Approach to Information Compression

The principle that the simplest model capable of describing observed phenomena should also correspond to the best description has long been a guiding rule of inference. In this paper a Bayesian approach to formally implementing this principle is employed to develop model selection criteria for detecting structural change in financial and economic time series. Model selection criteria which allow for multiple structural breaks and which seek the optimal model order and parameter choices within regimes are derived. Comparative simulations against other popular information based model selection criteria are performed. Application of the derived criteria are also made to example financial and economic time series.Complexity theory; segmentation; break points; change points; model selection; model choice.

Застосування методів нелінійного аналізу для побудови системи моніторінгу фондових ринків

Метою даної роботи є вирішення проблеми згладжування міри ламінарність рекурентного кількісного аналізу для побудови системи моніторингу фондових ринків

Прогнозирование существенно нестационарных многофакторных временных рядов на примере показателя инвестиций российских небанковских корпораций за рубеж

В данной работе предпринимается попытка разработки алгоритма, позволяющего прогнозировать будущие значения макроэкономических показателей, принимая во внимание нестационарность процессов при изменении структуры модели на примере показателя объема инвестиций российских небанковских корпораций за рубеж

Stability Selection of the Number of Clusters

Selecting the number of clusters is one of the greatest challenges in clustering analysis. In this thesis, we propose a variety of stability selection criteria based on cross validation for determining the number of clusters. Clustering stability measures the agreement of clusterings obtained by applying the same clustering algorithm on multiple independent and identically distributed samples. We propose to measure the clustering stability by the correlation between two clustering functions. These criteria are motivated by the concept of clustering instability proposed by Wang (2010), which is based on a form of clustering distance. In addition, the effectiveness and robustness of the proposed methods are numerically demonstrated on a variety of simulated and real world samples

A spectroscopy of texts for effective clustering

For many clustering algorithms, such as k-means, EM, and CLOPE, there is usually a requirement to set some parameters. Often, these parameters directly or indirectly control the number of clusters to return. In the presence of different data characteristics and analysis contexts, it is often difficult for the user to estimate the number of clusters in the data set. This is especially true in text collections such as Web documents, images or biological data. The fundamental question this paper addresses is: ldquoHow can we effectively estimate the natural number of clusters in a given text collection?rdquo. We propose to use spectral analysis, which analyzes the eigenvalues (not eigenvectors) of the collection, as the solution to the above. We first present the relationship between a text collection and its underlying spectra. We then show how the answer to this question enhances the clustering process. Finally, we conclude with empirical results and related work.<br /

Behavioural motifs of larval Drosophila melanogaster and Caenorhabditis elegans

I present a novel method for the unsupervised discovery of behavioural motifs in larval Drosophila melanogaster and Caenorhabditis elegans. Most current approaches to behavioural annotation suffer from the requirement of training data. As a result, automated programs carry the same observational biases as the humans who have annotated the data. The key novel element of my work is that it does not require training data; rather, behavioural motifs are discovered from the data itself. The method is based on an eigenshape representation of posture. Hence, my approach is called the eigenshape annotator (ESA). First, I examine the annotation consistency for a specific behaviour, the Omega turn of C. elegans, and find significant inconsistency in both expert annotation and the various Omega turn detection algorithms. This finding highlights the need for unbiased tools to study behaviour. A behavioural motif is defined as a particular sequence of postures that recurs frequently. In ESA, posture is represented by an eigenshape time series, and motifs are discovered in this representation. To find motifs, the time series is segmented, and the resulting segments are then clustered. The result is a set of self-similar time series segments, i.e. motifs. The advantage of this novel framework over the popular sliding windows approaches is twofold. First, it does not rely on the ‘closest neighbours’ definition of motifs, by which every motif has exactly two instances. Second, it does not require the assumption of exactly equal length for motifs of the same class. Behavioural motifs discovered using the segmentation-clustering framework are used as the basis of the ESA annotator. ESA is fully probabilistic, therefore avoiding rigid threshold values and allowing classification uncertainty to be quantified. I apply eigenshape annotation to both larval Drosophila and C. elegans, and produce a close match to hand annotation of behavioural states. However, many behavioural events cannot be unambiguously classified. By comparing the results to eigenshape annotation of an artificial agent’s behaviour, I argue that the ambiguity is due to greater continuity between behavioural states than is generally assumed for these organisms