9,294 research outputs found
Decomposing feature-level variation with Covariate Gaussian Process Latent Variable Models
The interpretation of complex high-dimensional data typically requires the
use of dimensionality reduction techniques to extract explanatory
low-dimensional representations. However, in many real-world problems these
representations may not be sufficient to aid interpretation on their own, and
it would be desirable to interpret the model in terms of the original features
themselves. Our goal is to characterise how feature-level variation depends on
latent low-dimensional representations, external covariates, and non-linear
interactions between the two. In this paper, we propose to achieve this through
a structured kernel decomposition in a hybrid Gaussian Process model which we
call the Covariate Gaussian Process Latent Variable Model (c-GPLVM). We
demonstrate the utility of our model on simulated examples and applications in
disease progression modelling from high-dimensional gene expression data in the
presence of additional phenotypes. In each setting we show how the c-GPLVM can
extract low-dimensional structures from high-dimensional data sets whilst
allowing a breakdown of feature-level variability that is not present in other
commonly used dimensionality reduction approaches
High-Dimensional Regression with Gaussian Mixtures and Partially-Latent Response Variables
In this work we address the problem of approximating high-dimensional data
with a low-dimensional representation. We make the following contributions. We
propose an inverse regression method which exchanges the roles of input and
response, such that the low-dimensional variable becomes the regressor, and
which is tractable. We introduce a mixture of locally-linear probabilistic
mapping model that starts with estimating the parameters of inverse regression,
and follows with inferring closed-form solutions for the forward parameters of
the high-dimensional regression problem of interest. Moreover, we introduce a
partially-latent paradigm, such that the vector-valued response variable is
composed of both observed and latent entries, thus being able to deal with data
contaminated by experimental artifacts that cannot be explained with noise
models. The proposed probabilistic formulation could be viewed as a
latent-variable augmentation of regression. We devise expectation-maximization
(EM) procedures based on a data augmentation strategy which facilitates the
maximum-likelihood search over the model parameters. We propose two
augmentation schemes and we describe in detail the associated EM inference
procedures that may well be viewed as generalizations of a number of EM
regression, dimension reduction, and factor analysis algorithms. The proposed
framework is validated with both synthetic and real data. We provide
experimental evidence that our method outperforms several existing regression
techniques
Dimensionality reduction of clustered data sets
We present a novel probabilistic latent variable model to perform linear dimensionality reduction on data sets which contain clusters. We prove that the maximum likelihood solution of the model is an unsupervised generalisation of linear discriminant analysis. This provides a completely new approach to one of the most established and widely used classification algorithms. The performance of the model is then demonstrated on a number of real and artificial data sets
Covariate dimension reduction for survival data via the Gaussian process latent variable model
The analysis of high dimensional survival data is challenging, primarily due
to the problem of overfitting which occurs when spurious relationships are
inferred from data that subsequently fail to exist in test data. Here we
propose a novel method of extracting a low dimensional representation of
covariates in survival data by combining the popular Gaussian Process Latent
Variable Model (GPLVM) with a Weibull Proportional Hazards Model (WPHM). The
combined model offers a flexible non-linear probabilistic method of detecting
and extracting any intrinsic low dimensional structure from high dimensional
data. By reducing the covariate dimension we aim to diminish the risk of
overfitting and increase the robustness and accuracy with which we infer
relationships between covariates and survival outcomes. In addition, we can
simultaneously combine information from multiple data sources by expressing
multiple datasets in terms of the same low dimensional space. We present
results from several simulation studies that illustrate a reduction in
overfitting and an increase in predictive performance, as well as successful
detection of intrinsic dimensionality. We provide evidence that it is
advantageous to combine dimensionality reduction with survival outcomes rather
than performing unsupervised dimensionality reduction on its own. Finally, we
use our model to analyse experimental gene expression data and detect and
extract a low dimensional representation that allows us to distinguish high and
low risk groups with superior accuracy compared to doing regression on the
original high dimensional data
Latent Fisher Discriminant Analysis
Linear Discriminant Analysis (LDA) is a well-known method for dimensionality
reduction and classification. Previous studies have also extended the
binary-class case into multi-classes. However, many applications, such as
object detection and keyframe extraction cannot provide consistent
instance-label pairs, while LDA requires labels on instance level for training.
Thus it cannot be directly applied for semi-supervised classification problem.
In this paper, we overcome this limitation and propose a latent variable Fisher
discriminant analysis model. We relax the instance-level labeling into
bag-level, is a kind of semi-supervised (video-level labels of event type are
required for semantic frame extraction) and incorporates a data-driven prior
over the latent variables. Hence, our method combines the latent variable
inference and dimension reduction in an unified bayesian framework. We test our
method on MUSK and Corel data sets and yield competitive results compared to
the baseline approach. We also demonstrate its capacity on the challenging
TRECVID MED11 dataset for semantic keyframe extraction and conduct a
human-factors ranking-based experimental evaluation, which clearly demonstrates
our proposed method consistently extracts more semantically meaningful
keyframes than challenging baselines.Comment: 12 page
Multi-view Learning as a Nonparametric Nonlinear Inter-Battery Factor Analysis
Factor analysis aims to determine latent factors, or traits, which summarize
a given data set. Inter-battery factor analysis extends this notion to multiple
views of the data. In this paper we show how a nonlinear, nonparametric version
of these models can be recovered through the Gaussian process latent variable
model. This gives us a flexible formalism for multi-view learning where the
latent variables can be used both for exploratory purposes and for learning
representations that enable efficient inference for ambiguous estimation tasks.
Learning is performed in a Bayesian manner through the formulation of a
variational compression scheme which gives a rigorous lower bound on the log
likelihood. Our Bayesian framework provides strong regularization during
training, allowing the structure of the latent space to be determined
efficiently and automatically. We demonstrate this by producing the first (to
our knowledge) published results of learning from dozens of views, even when
data is scarce. We further show experimental results on several different types
of multi-view data sets and for different kinds of tasks, including exploratory
data analysis, generation, ambiguity modelling through latent priors and
classification.Comment: 49 pages including appendi
Robust Head-Pose Estimation Based on Partially-Latent Mixture of Linear Regressions
Head-pose estimation has many applications, such as social event analysis,
human-robot and human-computer interaction, driving assistance, and so forth.
Head-pose estimation is challenging because it must cope with changing
illumination conditions, variabilities in face orientation and in appearance,
partial occlusions of facial landmarks, as well as bounding-box-to-face
alignment errors. We propose tu use a mixture of linear regressions with
partially-latent output. This regression method learns to map high-dimensional
feature vectors (extracted from bounding boxes of faces) onto the joint space
of head-pose angles and bounding-box shifts, such that they are robustly
predicted in the presence of unobservable phenomena. We describe in detail the
mapping method that combines the merits of unsupervised manifold learning
techniques and of mixtures of regressions. We validate our method with three
publicly available datasets and we thoroughly benchmark four variants of the
proposed algorithm with several state-of-the-art head-pose estimation methods.Comment: 12 pages, 5 figures, 3 table
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