22,623 research outputs found
Max-stable sketches: estimation of Lp-norms, dominance norms and point queries for non-negative signals
Max-stable random sketches can be computed efficiently on fast streaming
positive data sets by using only sequential access to the data. They can be
used to answer point and Lp-norm queries for the signal. There is an intriguing
connection between the so-called p-stable (or sum-stable) and the max-stable
sketches. Rigorous performance guarantees through error-probability estimates
are derived and the algorithmic implementation is discussed
Generative Adversarial Networks (GANs): Challenges, Solutions, and Future Directions
Generative Adversarial Networks (GANs) is a novel class of deep generative
models which has recently gained significant attention. GANs learns complex and
high-dimensional distributions implicitly over images, audio, and data.
However, there exists major challenges in training of GANs, i.e., mode
collapse, non-convergence and instability, due to inappropriate design of
network architecture, use of objective function and selection of optimization
algorithm. Recently, to address these challenges, several solutions for better
design and optimization of GANs have been investigated based on techniques of
re-engineered network architectures, new objective functions and alternative
optimization algorithms. To the best of our knowledge, there is no existing
survey that has particularly focused on broad and systematic developments of
these solutions. In this study, we perform a comprehensive survey of the
advancements in GANs design and optimization solutions proposed to handle GANs
challenges. We first identify key research issues within each design and
optimization technique and then propose a new taxonomy to structure solutions
by key research issues. In accordance with the taxonomy, we provide a detailed
discussion on different GANs variants proposed within each solution and their
relationships. Finally, based on the insights gained, we present the promising
research directions in this rapidly growing field.Comment: 42 pages, Figure 13, Table
Sketching for Large-Scale Learning of Mixture Models
Learning parameters from voluminous data can be prohibitive in terms of
memory and computational requirements. We propose a "compressive learning"
framework where we estimate model parameters from a sketch of the training
data. This sketch is a collection of generalized moments of the underlying
probability distribution of the data. It can be computed in a single pass on
the training set, and is easily computable on streams or distributed datasets.
The proposed framework shares similarities with compressive sensing, which aims
at drastically reducing the dimension of high-dimensional signals while
preserving the ability to reconstruct them. To perform the estimation task, we
derive an iterative algorithm analogous to sparse reconstruction algorithms in
the context of linear inverse problems. We exemplify our framework with the
compressive estimation of a Gaussian Mixture Model (GMM), providing heuristics
on the choice of the sketching procedure and theoretical guarantees of
reconstruction. We experimentally show on synthetic data that the proposed
algorithm yields results comparable to the classical Expectation-Maximization
(EM) technique while requiring significantly less memory and fewer computations
when the number of database elements is large. We further demonstrate the
potential of the approach on real large-scale data (over 10 8 training samples)
for the task of model-based speaker verification. Finally, we draw some
connections between the proposed framework and approximate Hilbert space
embedding of probability distributions using random features. We show that the
proposed sketching operator can be seen as an innovative method to design
translation-invariant kernels adapted to the analysis of GMMs. We also use this
theoretical framework to derive information preservation guarantees, in the
spirit of infinite-dimensional compressive sensing
On the accuracy of solving confluent Prony systems
In this paper we consider several nonlinear systems of algebraic equations
which can be called "Prony-type". These systems arise in various reconstruction
problems in several branches of theoretical and applied mathematics, such as
frequency estimation and nonlinear Fourier inversion. Consequently, the
question of stability of solution with respect to errors in the right-hand side
becomes critical for the success of any particular application. We investigate
the question of "maximal possible accuracy" of solving Prony-type systems,
putting stress on the "local" behavior which approximates situations with low
absolute measurement error. The accuracy estimates are formulated in very
simple geometric terms, shedding some light on the structure of the problem.
Numerical tests suggest that "global" solution techniques such as Prony's
algorithm and ESPRIT method are suboptimal when compared to this theoretical
"best local" behavior
Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)
The implicit objective of the biennial "international - Traveling Workshop on
Interactions between Sparse models and Technology" (iTWIST) is to foster
collaboration between international scientific teams by disseminating ideas
through both specific oral/poster presentations and free discussions. For its
second edition, the iTWIST workshop took place in the medieval and picturesque
town of Namur in Belgium, from Wednesday August 27th till Friday August 29th,
2014. The workshop was conveniently located in "The Arsenal" building within
walking distance of both hotels and town center. iTWIST'14 has gathered about
70 international participants and has featured 9 invited talks, 10 oral
presentations, and 14 posters on the following themes, all related to the
theory, application and generalization of the "sparsity paradigm":
Sparsity-driven data sensing and processing; Union of low dimensional
subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph
sensing/processing; Blind inverse problems and dictionary learning; Sparsity
and computational neuroscience; Information theory, geometry and randomness;
Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?;
Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website:
http://sites.google.com/site/itwist1
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