106,630 research outputs found
ImitAL: Learned Active Learning Strategy on Synthetic Data
Active Learning (AL) is a well-known standard method for efficiently
obtaining annotated data by first labeling the samples that contain the most
information based on a query strategy. In the past, a large variety of such
query strategies has been proposed, with each generation of new strategies
increasing the runtime and adding more complexity. However, to the best of our
our knowledge, none of these strategies excels consistently over a large number
of datasets from different application domains. Basically, most of the the
existing AL strategies are a combination of the two simple heuristics
informativeness and representativeness, and the big differences lie in the
combination of the often conflicting heuristics. Within this paper, we propose
ImitAL, a domain-independent novel query strategy, which encodes AL as a
learning-to-rank problem and learns an optimal combination between both
heuristics. We train ImitAL on large-scale simulated AL runs on purely
synthetic datasets. To show that ImitAL was successfully trained, we perform an
extensive evaluation comparing our strategy on 13 different datasets, from a
wide range of domains, with 7 other query strategies.Comment: arXiv admin note: text overlap with arXiv:2108.0767
Robust PCA as Bilinear Decomposition with Outlier-Sparsity Regularization
Principal component analysis (PCA) is widely used for dimensionality
reduction, with well-documented merits in various applications involving
high-dimensional data, including computer vision, preference measurement, and
bioinformatics. In this context, the fresh look advocated here permeates
benefits from variable selection and compressive sampling, to robustify PCA
against outliers. A least-trimmed squares estimator of a low-rank bilinear
factor analysis model is shown closely related to that obtained from an
-(pseudo)norm-regularized criterion encouraging sparsity in a matrix
explicitly modeling the outliers. This connection suggests robust PCA schemes
based on convex relaxation, which lead naturally to a family of robust
estimators encompassing Huber's optimal M-class as a special case. Outliers are
identified by tuning a regularization parameter, which amounts to controlling
sparsity of the outlier matrix along the whole robustification path of (group)
least-absolute shrinkage and selection operator (Lasso) solutions. Beyond its
neat ties to robust statistics, the developed outlier-aware PCA framework is
versatile to accommodate novel and scalable algorithms to: i) track the
low-rank signal subspace robustly, as new data are acquired in real time; and
ii) determine principal components robustly in (possibly) infinite-dimensional
feature spaces. Synthetic and real data tests corroborate the effectiveness of
the proposed robust PCA schemes, when used to identify aberrant responses in
personality assessment surveys, as well as unveil communities in social
networks, and intruders from video surveillance data.Comment: 30 pages, submitted to IEEE Transactions on Signal Processin
Randomized Dynamic Mode Decomposition
This paper presents a randomized algorithm for computing the near-optimal
low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging
techniques to compute low-rank matrix approximations at a fraction of the cost
of deterministic algorithms, easing the computational challenges arising in the
area of `big data'. The idea is to derive a small matrix from the
high-dimensional data, which is then used to efficiently compute the dynamic
modes and eigenvalues. The algorithm is presented in a modular probabilistic
framework, and the approximation quality can be controlled via oversampling and
power iterations. The effectiveness of the resulting randomized DMD algorithm
is demonstrated on several benchmark examples of increasing complexity,
providing an accurate and efficient approach to extract spatiotemporal coherent
structures from big data in a framework that scales with the intrinsic rank of
the data, rather than the ambient measurement dimension. For this work we
assume that the dynamics of the problem under consideration is evolving on a
low-dimensional subspace that is well characterized by a fast decaying singular
value spectrum
Regression and Singular Value Decomposition in Dynamic Graphs
Most of real-world graphs are {\em dynamic}, i.e., they change over time.
However, while problems such as regression and Singular Value Decomposition
(SVD) have been studied for {\em static} graphs, they have not been
investigated for {\em dynamic} graphs, yet. In this paper, we introduce,
motivate and study regression and SVD over dynamic graphs. First, we present
the notion of {\em update-efficient matrix embedding} that defines the
conditions sufficient for a matrix embedding to be used for the dynamic graph
regression problem (under norm). We prove that given an
update-efficient matrix embedding (e.g., adjacency matrix), after an update
operation in the graph, the optimal solution of the graph regression problem
for the revised graph can be computed in time. We also study dynamic
graph regression under least absolute deviation. Then, we characterize a class
of matrix embeddings that can be used to efficiently update SVD of a dynamic
graph. For adjacency matrix and Laplacian matrix, we study those graph update
operations for which SVD (and low rank approximation) can be updated
efficiently
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