2,657 research outputs found

    Time Series Cluster Kernel for Learning Similarities between Multivariate Time Series with Missing Data

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    Similarity-based approaches represent a promising direction for time series analysis. However, many such methods rely on parameter tuning, and some have shortcomings if the time series are multivariate (MTS), due to dependencies between attributes, or the time series contain missing data. In this paper, we address these challenges within the powerful context of kernel methods by proposing the robust \emph{time series cluster kernel} (TCK). The approach taken leverages the missing data handling properties of Gaussian mixture models (GMM) augmented with informative prior distributions. An ensemble learning approach is exploited to ensure robustness to parameters by combining the clustering results of many GMM to form the final kernel. We evaluate the TCK on synthetic and real data and compare to other state-of-the-art techniques. The experimental results demonstrate that the TCK is robust to parameter choices, provides competitive results for MTS without missing data and outstanding results for missing data.Comment: 23 pages, 6 figure

    Insights on Learning Tractable Probabilistic Graphical Models

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    Insights on Learning Tractable Probabilistic Graphical Models

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    On Practical machine Learning and Data Analysis

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    This thesis discusses and addresses some of the difficulties associated with practical machine learning and data analysis. Introducing data driven methods in e.g industrial and business applications can lead to large gains in productivity and efficiency, but the cost and complexity are often overwhelming. Creating machine learning applications in practise often involves a large amount of manual labour, which often needs to be performed by an experienced analyst without significant experience with the application area. We will here discuss some of the hurdles faced in a typical analysis project and suggest measures and methods to simplify the process. One of the most important issues when applying machine learning methods to complex data, such as e.g. industrial applications, is that the processes generating the data are modelled in an appropriate way. Relevant aspects have to be formalised and represented in a way that allow us to perform our calculations in an efficient manner. We present a statistical modelling framework, Hierarchical Graph Mixtures, based on a combination of graphical models and mixture models. It allows us to create consistent, expressive statistical models that simplify the modelling of complex systems. Using a Bayesian approach, we allow for encoding of prior knowledge and make the models applicable in situations when relatively little data are available. Detecting structures in data, such as clusters and dependency structure, is very important both for understanding an application area and for specifying the structure of e.g. a hierarchical graph mixture. We will discuss how this structure can be extracted for sequential data. By using the inherent dependency structure of sequential data we construct an information theoretical measure of correlation that does not suffer from the problems most common correlation measures have with this type of data. In many diagnosis situations it is desirable to perform a classification in an iterative and interactive manner. The matter is often complicated by very limited amounts of knowledge and examples when a new system to be diagnosed is initially brought into use. We describe how to create an incremental classification system based on a statistical model that is trained from empirical data, and show how the limited available background information can still be used initially for a functioning diagnosis system. To minimise the effort with which results are achieved within data analysis projects, we need to address not only the models used, but also the methodology and applications that can help simplify the process. We present a methodology for data preparation and a software library intended for rapid analysis, prototyping, and deployment. Finally, we will study a few example applications, presenting tasks within classification, prediction and anomaly detection. The examples include demand prediction for supply chain management, approximating complex simulators for increased speed in parameter optimisation, and fraud detection and classification within a media-on-demand system

    Apples and oranges: avoiding different priors in Bayesian DNA sequence analysis

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    <p>Abstract</p> <p>Background</p> <p>One of the challenges of bioinformatics remains the recognition of short signal sequences in genomic DNA such as donor or acceptor splice sites, splicing enhancers or silencers, translation initiation sites, transcription start sites, transcription factor binding sites, nucleosome binding sites, miRNA binding sites, or insulator binding sites. During the last decade, a wealth of algorithms for the recognition of such DNA sequences has been developed and compared with the goal of improving their performance and to deepen our understanding of the underlying cellular processes. Most of these algorithms are based on statistical models belonging to the family of Markov random fields such as position weight matrix models, weight array matrix models, Markov models of higher order, or moral Bayesian networks. While in many comparative studies different learning principles or different statistical models have been compared, the influence of choosing different prior distributions for the model parameters when using different learning principles has been overlooked, and possibly lead to questionable conclusions.</p> <p>Results</p> <p>With the goal of allowing direct comparisons of different learning principles for models from the family of Markov random fields based on the <it>same a-priori information</it>, we derive a generalization of the commonly-used product-Dirichlet prior. We find that the derived prior behaves like a Gaussian prior close to the maximum and like a Laplace prior in the far tails. In two case studies, we illustrate the utility of the derived prior for a direct comparison of different learning principles with different models for the recognition of binding sites of the transcription factor Sp1 and human donor splice sites.</p> <p>Conclusions</p> <p>We find that comparisons of different learning principles using the same a-priori information can lead to conclusions different from those of previous studies in which the effect resulting from different priors has been neglected. We implement the derived prior is implemented in the open-source library Jstacs to enable an easy application to comparative studies of different learning principles in the field of sequence analysis.</p

    Graphical models for visual object recognition and tracking

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    Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 277-301).We develop statistical methods which allow effective visual detection, categorization, and tracking of objects in complex scenes. Such computer vision systems must be robust to wide variations in object appearance, the often small size of training databases, and ambiguities induced by articulated or partially occluded objects. Graphical models provide a powerful framework for encoding the statistical structure of visual scenes, and developing corresponding learning and inference algorithms. In this thesis, we describe several models which integrate graphical representations with nonparametric statistical methods. This approach leads to inference algorithms which tractably recover high-dimensional, continuous object pose variations, and learning procedures which transfer knowledge among related recognition tasks. Motivated by visual tracking problems, we first develop a nonparametric extension of the belief propagation (BP) algorithm. Using Monte Carlo methods, we provide general procedures for recursively updating particle-based approximations of continuous sufficient statistics. Efficient multiscale sampling methods then allow this nonparametric BP algorithm to be flexibly adapted to many different applications.(cont.) As a particular example, we consider a graphical model describing the hand's three-dimensional (3D) structure, kinematics, and dynamics. This graph encodes global hand pose via the 3D position and orientation of several rigid components, and thus exposes local structure in a high-dimensional articulated model. Applying nonparametric BP, we recover a hand tracking algorithm which is robust to outliers and local visual ambiguities. Via a set of latent occupancy masks, we also extend our approach to consistently infer occlusion events in a distributed fashion. In the second half of this thesis, we develop methods for learning hierarchical models of objects, the parts composing them, and the scenes surrounding them. Our approach couples topic models originally developed for text analysis with spatial transformations, and thus consistently accounts for geometric constraints. By building integrated scene models, we may discover contextual relationships, and better exploit partially labeled training images. We first consider images of isolated objects, and show that sharing parts among object categories improves accuracy when learning from few examples.(cont.) Turning to multiple object scenes, we propose nonparametric models which use Dirichlet processes to automatically learn the number of parts underlying each object category, and objects composing each scene. Adapting these transformed Dirichlet processes to images taken with a binocular stereo camera, we learn integrated, 3D models of object geometry and appearance. This leads to a Monte Carlo algorithm which automatically infers 3D scene structure from the predictable geometry of known object categories.by Erik B. Sudderth.Ph.D

    Data clustering using a model granular magnet

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    We present a new approach to clustering, based on the physical properties of an inhomogeneous ferromagnet. No assumption is made regarding the underlying distribution of the data. We assign a Potts spin to each data point and introduce an interaction between neighboring points, whose strength is a decreasing function of the distance between the neighbors. This magnetic system exhibits three phases. At very low temperatures it is completely ordered; all spins are aligned. At very high temperatures the system does not exhibit any ordering and in an intermediate regime clusters of relatively strongly coupled spins become ordered, whereas different clusters remain uncorrelated. This intermediate phase is identified by a jump in the order parameters. The spin-spin correlation function is used to partition the spins and the corresponding data points into clusters. We demonstrate on three synthetic and three real data sets how the method works. Detailed comparison to the performance of other techniques clearly indicates the relative success of our method.Comment: 46 pages, postscript, 15 ps figures include
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