1,077 research outputs found
Perceptually-Driven Video Coding with the Daala Video Codec
The Daala project is a royalty-free video codec that attempts to compete with
the best patent-encumbered codecs. Part of our strategy is to replace core
tools of traditional video codecs with alternative approaches, many of them
designed to take perceptual aspects into account, rather than optimizing for
simple metrics like PSNR. This paper documents some of our experiences with
these tools, which ones worked and which did not. We evaluate which tools are
easy to integrate into a more traditional codec design, and show results in the
context of the codec being developed by the Alliance for Open Media.Comment: 19 pages, Proceedings of SPIE Workshop on Applications of Digital
Image Processing (ADIP), 201
Conditioning of Random Block Subdictionaries with Applications to Block-Sparse Recovery and Regression
The linear model, in which a set of observations is assumed to be given by a
linear combination of columns of a matrix, has long been the mainstay of the
statistics and signal processing literature. One particular challenge for
inference under linear models is understanding the conditions on the dictionary
under which reliable inference is possible. This challenge has attracted
renewed attention in recent years since many modern inference problems deal
with the "underdetermined" setting, in which the number of observations is much
smaller than the number of columns in the dictionary. This paper makes several
contributions for this setting when the set of observations is given by a
linear combination of a small number of groups of columns of the dictionary,
termed the "block-sparse" case. First, it specifies conditions on the
dictionary under which most block subdictionaries are well conditioned. This
result is fundamentally different from prior work on block-sparse inference
because (i) it provides conditions that can be explicitly computed in
polynomial time, (ii) the given conditions translate into near-optimal scaling
of the number of columns of the block subdictionaries as a function of the
number of observations for a large class of dictionaries, and (iii) it suggests
that the spectral norm and the quadratic-mean block coherence of the dictionary
(rather than the worst-case coherences) fundamentally limit the scaling of
dimensions of the well-conditioned block subdictionaries. Second, this paper
investigates the problems of block-sparse recovery and block-sparse regression
in underdetermined settings. Near-optimal block-sparse recovery and regression
are possible for certain dictionaries as long as the dictionary satisfies
easily computable conditions and the coefficients describing the linear
combination of groups of columns can be modeled through a mild statistical
prior.Comment: 39 pages, 3 figures. A revised and expanded version of the paper
published in IEEE Transactions on Information Theory (DOI:
10.1109/TIT.2015.2429632); this revision includes corrections in the proofs
of some of the result
Control and optimization methods in biomedical systems: from cells to humans
Optimization and control theory are well developed techniques to quantize, model, understand and optimize real world systems and they have been widely used in engineering, economics, and science. In this thesis, we focus on applications in biomedical systems ranging from cells to microbial communities, and to something as complex as the human body.
The first problem we consider is that of medication dosage control for drugs delivered intravenously to the patient. We focus specifically on a blood thinner (called bivalirudin) used in the post cardiac surgery Intensive Care Unit (ICU). We develop two approaches (a model-free and a model-based one) that predict the effect of bivalirudin. After obtaining the model and its best fit parameters by solving a non-linear optimization problem, we develop automatic dosage controllers that adaptively regulate its effect to desired levels. Our algorithms are validated using actual data from a large hospital in the Boston area.
In the second problem, we introduce a cellular objective function inference mechanism in metabolic networks. We develop an inverse optimization method, called InvFBA (Inverse Flux Balance Analysis), to infer the objective functions of growing cells by using their reaction fluxes. InvFBA can be seen as an inverse version of FBA (Flux Balance Analysis) which predicts the distribution of the cell's reaction fluxes by using a hypothetical objective function. The objective functions can be linear, quadratic and non-parametric. The efficiency of the InvFBA approach matches the structure of the FBA and ensures scalability to large networks and optimality of the solution. After testing our algorithm on simulated E. coli data and time-dependent S. oneidensis fluxes inferred from gene expression data, we apply our inverse approach to flux measurements in long-term evolved E. coli strains, revealing objective functions that provide insight into metabolic adaptation trajectories.
In the final problem in this thesis, we formulate a novel resource allocation problem in microbial ecosystems. We consider a given number of microbial species living symbiotically in a community and a list of all metabolic reactions present in the community, expressed in terms of the metabolite proportions involved in each reaction.
We are interested in allocating reactions to organisms so that each organism maintains a minimal level of growth and the community optimizes certain objectives, such as maximizing growth and/or the uptake of specific compounds from the common environment. We leverage tools from Flux Balance Analysis (FBA) and formulate the problem as a mixed integer linear programming problem. We test our method in a toy
model involving two organisms that can only survive through cross-feeding, demonstrating that the method can recover this interaction. We also test the method in a community of two simplified bacteria described in terms of their core, simplified metabolic network. We demonstrate that the method can obtain syntrophic cross-feeding species that would be very difficult to design manually
Approaches for Outlier Detection in Sparse High-Dimensional Regression Models
Modern regression studies often encompass a very large number of potential predictors,
possibly larger than the sample size, and sometimes growing with the sample
size itself. This increases the chances that a substantial portion of the predictors
is redundant, as well as the risk of data contamination. Tackling these problems is
of utmost importance to facilitate scientific discoveries, since model estimates are
highly sensitive both to the choice of predictors and to the presence of outliers. In
this thesis, we contribute to this area considering the problem of robust model selection
in a variety of settings, where outliers may arise both in the response and
the predictors. Our proposals simplify model interpretation, guarantee predictive
performance, and allow us to study and control the influence of outlying cases on
the fit.
First, we consider the co-occurrence of multiple mean-shift and variance-inflation
outliers in low-dimensional linear models. We rely on robust estimation techniques
to identify outliers of each type, exclude mean-shift outliers, and use restricted
maximum likelihood estimation to down-weight and accommodate variance-inflation
outliers into the model fit. Second, we extend our setting to high-dimensional linear
models. We show that mean-shift and variance-inflation outliers can be modeled as
additional fixed and random components, respectively, and evaluated independently.
Specifically, we perform feature selection and mean-shift outlier detection through
a robust class of nonconcave penalization methods, and variance-inflation outlier
detection through the penalization of the restricted posterior mode. The resulting
approach satisfies a robust oracle property for feature selection in the presence of
data contamination – which allows the number of features to exponentially increase
with the sample size – and detects truly outlying cases of each type with asymptotic
probability one. This provides an optimal trade-off between a high breakdown point
and efficiency. Third, focusing on high-dimensional linear models affected by meanshift
outliers, we develop a general framework in which L0-constraints coupled with
mixed-integer programming techniques are used to perform simultaneous feature
selection and outlier detection with provably optimal guarantees. In particular,
we provide necessary and sufficient conditions for a robustly strong oracle property,
where again the number of features can increase exponentially with the sample size,
and prove optimality for parameter estimation and the resulting breakdown point.
Finally, we consider generalized linear models and rely on logistic slippage to perform
outlier detection and removal in binary classification. Here we use L0-constraints
and mixed-integer conic programming techniques to solve the underlying double
combinatorial problem of feature selection and outlier detection, and the framework
allows us again to pursue optimality guarantees.
For all the proposed approaches, we also provide computationally lean heuristic
algorithms, tuning procedures, and diagnostic tools which help to guide the analysis.
We consider several real-world applications, including the study of the relationships
between childhood obesity and the human microbiome, and of the main drivers of
honey bee loss. All methods developed and data used, as well as the source code to
replicate our analyses, are publicly available
Recommender Systems
The ongoing rapid expansion of the Internet greatly increases the necessity
of effective recommender systems for filtering the abundant information.
Extensive research for recommender systems is conducted by a broad range of
communities including social and computer scientists, physicists, and
interdisciplinary researchers. Despite substantial theoretical and practical
achievements, unification and comparison of different approaches are lacking,
which impedes further advances. In this article, we review recent developments
in recommender systems and discuss the major challenges. We compare and
evaluate available algorithms and examine their roles in the future
developments. In addition to algorithms, physical aspects are described to
illustrate macroscopic behavior of recommender systems. Potential impacts and
future directions are discussed. We emphasize that recommendation has a great
scientific depth and combines diverse research fields which makes it of
interests for physicists as well as interdisciplinary researchers.Comment: 97 pages, 20 figures (To appear in Physics Reports
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