5,202 research outputs found
Learning Models over Relational Data using Sparse Tensors and Functional Dependencies
Integrated solutions for analytics over relational databases are of great
practical importance as they avoid the costly repeated loop data scientists
have to deal with on a daily basis: select features from data residing in
relational databases using feature extraction queries involving joins,
projections, and aggregations; export the training dataset defined by such
queries; convert this dataset into the format of an external learning tool; and
train the desired model using this tool. These integrated solutions are also a
fertile ground of theoretically fundamental and challenging problems at the
intersection of relational and statistical data models.
This article introduces a unified framework for training and evaluating a
class of statistical learning models over relational databases. This class
includes ridge linear regression, polynomial regression, factorization
machines, and principal component analysis. We show that, by synergizing key
tools from database theory such as schema information, query structure,
functional dependencies, recent advances in query evaluation algorithms, and
from linear algebra such as tensor and matrix operations, one can formulate
relational analytics problems and design efficient (query and data)
structure-aware algorithms to solve them.
This theoretical development informed the design and implementation of the
AC/DC system for structure-aware learning. We benchmark the performance of
AC/DC against R, MADlib, libFM, and TensorFlow. For typical retail forecasting
and advertisement planning applications, AC/DC can learn polynomial regression
models and factorization machines with at least the same accuracy as its
competitors and up to three orders of magnitude faster than its competitors
whenever they do not run out of memory, exceed 24-hour timeout, or encounter
internal design limitations.Comment: 61 pages, 9 figures, 2 table
Probabilistic Inference from Arbitrary Uncertainty using Mixtures of Factorized Generalized Gaussians
This paper presents a general and efficient framework for probabilistic
inference and learning from arbitrary uncertain information. It exploits the
calculation properties of finite mixture models, conjugate families and
factorization. Both the joint probability density of the variables and the
likelihood function of the (objective or subjective) observation are
approximated by a special mixture model, in such a way that any desired
conditional distribution can be directly obtained without numerical
integration. We have developed an extended version of the expectation
maximization (EM) algorithm to estimate the parameters of mixture models from
uncertain training examples (indirect observations). As a consequence, any
piece of exact or uncertain information about both input and output values is
consistently handled in the inference and learning stages. This ability,
extremely useful in certain situations, is not found in most alternative
methods. The proposed framework is formally justified from standard
probabilistic principles and illustrative examples are provided in the fields
of nonparametric pattern classification, nonlinear regression and pattern
completion. Finally, experiments on a real application and comparative results
over standard databases provide empirical evidence of the utility of the method
in a wide range of applications
Robust Principal Component Analysis on Graphs
Principal Component Analysis (PCA) is the most widely used tool for linear
dimensionality reduction and clustering. Still it is highly sensitive to
outliers and does not scale well with respect to the number of data samples.
Robust PCA solves the first issue with a sparse penalty term. The second issue
can be handled with the matrix factorization model, which is however
non-convex. Besides, PCA based clustering can also be enhanced by using a graph
of data similarity. In this article, we introduce a new model called "Robust
PCA on Graphs" which incorporates spectral graph regularization into the Robust
PCA framework. Our proposed model benefits from 1) the robustness of principal
components to occlusions and missing values, 2) enhanced low-rank recovery, 3)
improved clustering property due to the graph smoothness assumption on the
low-rank matrix, and 4) convexity of the resulting optimization problem.
Extensive experiments on 8 benchmark, 3 video and 2 artificial datasets with
corruptions clearly reveal that our model outperforms 10 other state-of-the-art
models in its clustering and low-rank recovery tasks
Improving Facial Analysis and Performance Driven Animation through Disentangling Identity and Expression
We present techniques for improving performance driven facial animation,
emotion recognition, and facial key-point or landmark prediction using learned
identity invariant representations. Established approaches to these problems
can work well if sufficient examples and labels for a particular identity are
available and factors of variation are highly controlled. However, labeled
examples of facial expressions, emotions and key-points for new individuals are
difficult and costly to obtain. In this paper we improve the ability of
techniques to generalize to new and unseen individuals by explicitly modeling
previously seen variations related to identity and expression. We use a
weakly-supervised approach in which identity labels are used to learn the
different factors of variation linked to identity separately from factors
related to expression. We show how probabilistic modeling of these sources of
variation allows one to learn identity-invariant representations for
expressions which can then be used to identity-normalize various procedures for
facial expression analysis and animation control. We also show how to extend
the widely used techniques of active appearance models and constrained local
models through replacing the underlying point distribution models which are
typically constructed using principal component analysis with
identity-expression factorized representations. We present a wide variety of
experiments in which we consistently improve performance on emotion
recognition, markerless performance-driven facial animation and facial
key-point tracking.Comment: to appear in Image and Vision Computing Journal (IMAVIS
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