82,140 research outputs found
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
Hyper-Spectral Image Analysis with Partially-Latent Regression and Spatial Markov Dependencies
Hyper-spectral data can be analyzed to recover physical properties at large
planetary scales. This involves resolving inverse problems which can be
addressed within machine learning, with the advantage that, once a relationship
between physical parameters and spectra has been established in a data-driven
fashion, the learned relationship can be used to estimate physical parameters
for new hyper-spectral observations. Within this framework, we propose a
spatially-constrained and partially-latent regression method which maps
high-dimensional inputs (hyper-spectral images) onto low-dimensional responses
(physical parameters such as the local chemical composition of the soil). The
proposed regression model comprises two key features. Firstly, it combines a
Gaussian mixture of locally-linear mappings (GLLiM) with a partially-latent
response model. While the former makes high-dimensional regression tractable,
the latter enables to deal with physical parameters that cannot be observed or,
more generally, with data contaminated by experimental artifacts that cannot be
explained with noise models. Secondly, spatial constraints are introduced in
the model through a Markov random field (MRF) prior which provides a spatial
structure to the Gaussian-mixture hidden variables. Experiments conducted on a
database composed of remotely sensed observations collected from the Mars
planet by the Mars Express orbiter demonstrate the effectiveness of the
proposed model.Comment: 12 pages, 4 figures, 3 table
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
Machine Learning and Integrative Analysis of Biomedical Big Data.
Recent developments in high-throughput technologies have accelerated the accumulation of massive amounts of omics data from multiple sources: genome, epigenome, transcriptome, proteome, metabolome, etc. Traditionally, data from each source (e.g., genome) is analyzed in isolation using statistical and machine learning (ML) methods. Integrative analysis of multi-omics and clinical data is key to new biomedical discoveries and advancements in precision medicine. However, data integration poses new computational challenges as well as exacerbates the ones associated with single-omics studies. Specialized computational approaches are required to effectively and efficiently perform integrative analysis of biomedical data acquired from diverse modalities. In this review, we discuss state-of-the-art ML-based approaches for tackling five specific computational challenges associated with integrative analysis: curse of dimensionality, data heterogeneity, missing data, class imbalance and scalability issues
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