2,483 research outputs found
"Influence Sketching": Finding Influential Samples In Large-Scale Regressions
There is an especially strong need in modern large-scale data analysis to
prioritize samples for manual inspection. For example, the inspection could
target important mislabeled samples or key vulnerabilities exploitable by an
adversarial attack. In order to solve the "needle in the haystack" problem of
which samples to inspect, we develop a new scalable version of Cook's distance,
a classical statistical technique for identifying samples which unusually
strongly impact the fit of a regression model (and its downstream predictions).
In order to scale this technique up to very large and high-dimensional
datasets, we introduce a new algorithm which we call "influence sketching."
Influence sketching embeds random projections within the influence computation;
in particular, the influence score is calculated using the randomly projected
pseudo-dataset from the post-convergence Generalized Linear Model (GLM). We
validate that influence sketching can reliably and successfully discover
influential samples by applying the technique to a malware detection dataset of
over 2 million executable files, each represented with almost 100,000 features.
For example, we find that randomly deleting approximately 10% of training
samples reduces predictive accuracy only slightly from 99.47% to 99.45%,
whereas deleting the same number of samples with high influence sketch scores
reduces predictive accuracy all the way down to 90.24%. Moreover, we find that
influential samples are especially likely to be mislabeled. In the case study,
we manually inspect the most influential samples, and find that influence
sketching pointed us to new, previously unidentified pieces of malware.Comment: fixed additional typo
Sparse Modeling for Image and Vision Processing
In recent years, a large amount of multi-disciplinary research has been
conducted on sparse models and their applications. In statistics and machine
learning, the sparsity principle is used to perform model selection---that is,
automatically selecting a simple model among a large collection of them. In
signal processing, sparse coding consists of representing data with linear
combinations of a few dictionary elements. Subsequently, the corresponding
tools have been widely adopted by several scientific communities such as
neuroscience, bioinformatics, or computer vision. The goal of this monograph is
to offer a self-contained view of sparse modeling for visual recognition and
image processing. More specifically, we focus on applications where the
dictionary is learned and adapted to data, yielding a compact representation
that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics
and Visio
Sparse Bilinear Logistic Regression
In this paper, we introduce the concept of sparse bilinear logistic
regression for decision problems involving explanatory variables that are
two-dimensional matrices. Such problems are common in computer vision,
brain-computer interfaces, style/content factorization, and parallel factor
analysis. The underlying optimization problem is bi-convex; we study its
solution and develop an efficient algorithm based on block coordinate descent.
We provide a theoretical guarantee for global convergence and estimate the
asymptotical convergence rate using the Kurdyka-{\L}ojasiewicz inequality. A
range of experiments with simulated and real data demonstrate that sparse
bilinear logistic regression outperforms current techniques in several
important applications.Comment: 27 pages, 5 figure
Distributed Low-rank Subspace Segmentation
Vision problems ranging from image clustering to motion segmentation to
semi-supervised learning can naturally be framed as subspace segmentation
problems, in which one aims to recover multiple low-dimensional subspaces from
noisy and corrupted input data. Low-Rank Representation (LRR), a convex
formulation of the subspace segmentation problem, is provably and empirically
accurate on small problems but does not scale to the massive sizes of modern
vision datasets. Moreover, past work aimed at scaling up low-rank matrix
factorization is not applicable to LRR given its non-decomposable constraints.
In this work, we propose a novel divide-and-conquer algorithm for large-scale
subspace segmentation that can cope with LRR's non-decomposable constraints and
maintains LRR's strong recovery guarantees. This has immediate implications for
the scalability of subspace segmentation, which we demonstrate on a benchmark
face recognition dataset and in simulations. We then introduce novel
applications of LRR-based subspace segmentation to large-scale semi-supervised
learning for multimedia event detection, concept detection, and image tagging.
In each case, we obtain state-of-the-art results and order-of-magnitude speed
ups
- …