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In this contribution, we propose a generic online (also sometimes called
adaptive or recursive) version of the Expectation-Maximisation (EM) algorithm
applicable to latent variable models of independent observations. Compared to
the algorithm of Titterington (1984), this approach is more directly connected
to the usual EM algorithm and does not rely on integration with respect to the
complete data distribution. The resulting algorithm is usually simpler and is
shown to achieve convergence to the stationary points of the Kullback-Leibler
divergence between the marginal distribution of the observation and the model
distribution at the optimal rate, i.e., that of the maximum likelihood
estimator. In addition, the proposed approach is also suitable for conditional
(or regression) models, as illustrated in the case of the mixture of linear
regressions model.
| 2,017 |
Online EM Algorithm for Latent Data Models | 2,017 |
We define a new model of quantum learning that we call Predictive Quantum
(PQ). This is a quantum analogue of PAC, where during the testing phase the
student is only required to answer a polynomial number of testing queries.
We demonstrate a relational concept class that is efficiently learnable in
PQ, while in any "reasonable" classical model exponential amount of training
data would be required. This is the first unconditional separation between
quantum and classical learning.
We show that our separation is the best possible in several ways; in
particular, there is no analogous result for a functional class, as well as for
several weaker versions of quantum learning. In order to demonstrate tightness
of our separation we consider a special case of one-way communication that we
call single-input mode, where Bob receives no input. Somewhat surprisingly,
this setting becomes nontrivial when relational communication tasks are
considered. In particular, any problem with two-sided input can be transformed
into a single-input relational problem of equal classical one-way cost. We show
that the situation is different in the quantum case, where the same
transformation can make the communication complexity exponentially larger. This
happens if and only if the original problem has exponential gap between quantum
and classical one-way communication costs. We believe that these auxiliary
results might be of independent interest.
| 2,012 |
Quantum Predictive Learning and Communication Complexity with Single
Input | 2,012 |
Cilibrasi and Vitanyi have demonstrated that it is possible to extract the
meaning of words from the world-wide web. To achieve this, they rely on the
number of webpages that are found through a Google search containing a given
word and they associate the page count to the probability that the word appears
on a webpage. Thus, conditional probabilities allow them to correlate one word
with another word's meaning. Furthermore, they have developed a similarity
distance function that gauges how closely related a pair of words is. We
present a specific counterexample to the triangle inequality for this
similarity distance function.
| 2,015 |
Google distance between words | 2,015 |
This paper has been retracted.
| 2,013 |
Differential Contrastive Divergence | 2,013 |
Given a matrix M of low-rank, we consider the problem of reconstructing it
from noisy observations of a small, random subset of its entries. The problem
arises in a variety of applications, from collaborative filtering (the `Netflix
problem') to structure-from-motion and positioning. We study a low complexity
algorithm introduced by Keshavan et al.(2009), based on a combination of
spectral techniques and manifold optimization, that we call here OptSpace. We
prove performance guarantees that are order-optimal in a number of
circumstances.
| 2,012 |
Matrix Completion from Noisy Entries | 2,012 |
Background: Hidden Markov models are widely employed by numerous
bioinformatics programs used today. Applications range widely from comparative
gene prediction to time-series analyses of micro-array data. The parameters of
the underlying models need to be adjusted for specific data sets, for example
the genome of a particular species, in order to maximize the prediction
accuracy. Computationally efficient algorithms for parameter training are thus
key to maximizing the usability of a wide range of bioinformatics applications.
Results: We introduce two computationally efficient training algorithms, one
for Viterbi training and one for stochastic expectation maximization (EM)
training, which render the memory requirements independent of the sequence
length. Unlike the existing algorithms for Viterbi and stochastic EM training
which require a two-step procedure, our two new algorithms require only one
step and scan the input sequence in only one direction. We also implement these
two new algorithms and the already published linear-memory algorithm for EM
training into the hidden Markov model compiler HMM-Converter and examine their
respective practical merits for three small example models.
Conclusions: Bioinformatics applications employing hidden Markov models can
use the two algorithms in order to make Viterbi training and stochastic EM
training more computationally efficient. Using these algorithms, parameter
training can thus be attempted for more complex models and longer training
sequences. The two new algorithms have the added advantage of being easier to
implement than the corresponding default algorithms for Viterbi training and
stochastic EM training.
| 2,012 |
Efficient algorithms for training the parameters of hidden Markov models
using stochastic expectation maximization EM training and Viterbi training | 2,012 |
There are many resources useful for processing images, most of them freely
available and quite friendly to use. In spite of this abundance of tools, a
study of the processing methods is still worthy of efforts. Here, we want to
discuss the possibilities arising from the use of fractional differential
calculus. This calculus evolved in the research field of pure mathematics until
1920, when applied science started to use it. Only recently, fractional
calculus was involved in image processing methods. As we shall see, the
fractional calculation is able to enhance the quality of images, with
interesting possibilities in edge detection and image restoration. We suggest
also the fractional differentiation as a tool to reveal faint objects in
astronomical images.
| 2,015 |
Fractional differentiation based image processing | 2,015 |
The versatility of exponential families, along with their attendant convexity
properties, make them a popular and effective statistical model. A central
issue is learning these models in high-dimensions, such as when there is some
sparsity pattern of the optimal parameter. This work characterizes a certain
strong convexity property of general exponential families, which allow their
generalization ability to be quantified. In particular, we show how this
property can be used to analyze generic exponential families under L_1
regularization.
| 2,015 |
Learning Exponential Families in High-Dimensions: Strong Convexity and
Sparsity | 2,015 |
This paper describes a methodology for detecting anomalies from sequentially
observed and potentially noisy data. The proposed approach consists of two main
elements: (1) {\em filtering}, or assigning a belief or likelihood to each
successive measurement based upon our ability to predict it from previous noisy
observations, and (2) {\em hedging}, or flagging potential anomalies by
comparing the current belief against a time-varying and data-adaptive
threshold. The threshold is adjusted based on the available feedback from an
end user. Our algorithms, which combine universal prediction with recent work
on online convex programming, do not require computing posterior distributions
given all current observations and involve simple primal-dual parameter
updates. At the heart of the proposed approach lie exponential-family models
which can be used in a wide variety of contexts and applications, and which
yield methods that achieve sublinear per-round regret against both static and
slowly varying product distributions with marginals drawn from the same
exponential family. Moreover, the regret against static distributions coincides
with the minimax value of the corresponding online strongly convex game. We
also prove bounds on the number of mistakes made during the hedging step
relative to the best offline choice of the threshold with access to all
estimated beliefs and feedback signals. We validate the theory on synthetic
data drawn from a time-varying distribution over binary vectors of high
dimensionality, as well as on the Enron email dataset.
| 2,012 |
Sequential anomaly detection in the presence of noise and limited
feedback | 2,012 |
Languages evolve over time in a process in which reproduction, mutation and
extinction are all possible, similar to what happens to living organisms. Using
this similarity it is possible, in principle, to build family trees which show
the degree of relatedness between languages.
The method used by modern glottochronology, developed by Swadesh in the
1950s, measures distances from the percentage of words with a common historical
origin. The weak point of this method is that subjective judgment plays a
relevant role.
Recently we proposed an automated method that avoids the subjectivity, whose
results can be replicated by studies that use the same database and that
doesn't require a specific linguistic knowledge. Moreover, the method allows a
quick comparison of a large number of languages.
We applied our method to the Indo-European and Austronesian families,
considering in both cases, fifty different languages. The resulting trees are
similar to those of previous studies, but with some important differences in
the position of few languages and subgroups. We believe that these differences
carry new information on the structure of the tree and on the phylogenetic
relationships within families.
| 2,012 |
Automated languages phylogeny from Levenshtein distance | 2,012 |
Analogical reasoning depends fundamentally on the ability to learn and
generalize about relations between objects. We develop an approach to
relational learning which, given a set of pairs of objects
$\mathbf{S}=\{A^{(1)}:B^{(1)},A^{(2)}:B^{(2)},\ldots,A^{(N)}:B ^{(N)}\}$,
measures how well other pairs A:B fit in with the set $\mathbf{S}$. Our work
addresses the following question: is the relation between objects A and B
analogous to those relations found in $\mathbf{S}$? Such questions are
particularly relevant in information retrieval, where an investigator might
want to search for analogous pairs of objects that match the query set of
interest. There are many ways in which objects can be related, making the task
of measuring analogies very challenging. Our approach combines a similarity
measure on function spaces with Bayesian analysis to produce a ranking. It
requires data containing features of the objects of interest and a link matrix
specifying which relationships exist; no further attributes of such
relationships are necessary. We illustrate the potential of our method on text
analysis and information networks. An application on discovering functional
interactions between pairs of proteins is discussed in detail, where we show
that our approach can work in practice even if a small set of protein pairs is
provided.
| 2,013 |
Ranking relations using analogies in biological and information networks | 2,013 |
We consider a group of Bayesian agents who try to estimate a state of the
world $\theta$ through interaction on a social network. Each agent $v$
initially receives a private measurement of $\theta$: a number $S_v$ picked
from a Gaussian distribution with mean $\theta$ and standard deviation one.
Then, in each discrete time iteration, each reveals its estimate of $\theta$ to
its neighbors, and, observing its neighbors' actions, updates its belief using
Bayes' Law.
This process aggregates information efficiently, in the sense that all the
agents converge to the belief that they would have, had they access to all the
private measurements. We show that this process is computationally efficient,
so that each agent's calculation can be easily carried out. We also show that
on any graph the process converges after at most $2N \cdot D$ steps, where $N$
is the number of agents and $D$ is the diameter of the network. Finally, we
show that on trees and on distance transitive-graphs the process converges
after $D$ steps, and that it preserves privacy, so that agents learn very
little about the private signal of most other agents, despite the efficient
aggregation of information. Our results extend those in an unpublished
manuscript of the first and last authors.
| 2,016 |
Efficient Bayesian Learning in Social Networks with Gaussian Estimators | 2,016 |
Automatic License Plate Recognition (ALPR) is a challenging area of research
due to its importance to variety of commercial applications. The overall
problem may be subdivided into two key modules, firstly, localization of
license plates from vehicle images, and secondly, optical character recognition
of extracted license plates. In the current work, we have concentrated on the
first part of the problem, i.e., localization of license plate regions from
Indian commercial vehicles as a significant step towards development of a
complete ALPR system for Indian vehicles. The technique is based on color based
segmentation of vehicle images and identification of potential license plate
regions. True license plates are finally localized based on four spatial and
horizontal contrast features. The technique successfully localizes the actual
license plates in 73.4% images.
| 2,015 |
An Offline Technique for Localization of License Plates for Indian
Commercial Vehicles | 2,015 |
Integrated Traffic Management Systems (ITMS) are now implemented in different
cities in India to primarily address the concerns of road-safety and security.
An automated Red Light Violation Detection System (RLVDS) is an integral part
of the ITMS. In our present work we have designed and developed a complete
system for generating the list of all stop-line violating vehicle images
automatically from video snapshots of road-side surveillance cameras. The
system first generates adaptive background images for each camera view,
subtracts captured images from the corresponding background images and analyses
potential occlusions over the stop-line in a traffic signal. Considering
round-the-clock operations in a real-life test environment, the developed
system could successfully track 92% images of vehicles with violations on the
stop-line in a "Red" traffic signal.
| 2,015 |
Development of an automated Red Light Violation Detection System (RLVDS)
for Indian vehicles | 2,015 |
Automatic License Plate Recognition system is a challenging area of research
now-a-days and binarization is an integral and most important part of it. In
case of a real life scenario, most of existing methods fail to properly
binarize the image of a vehicle in a congested road, captured through a CCD
camera. In the current work we have applied histogram equalization technique
over the complete image and also over different hierarchy of image
partitioning. A novel scheme is formulated for giving the membership value to
each pixel for each hierarchy of histogram equalization. Then the image is
binarized depending on the net membership value of each pixel. The technique is
exhaustively evaluated on the vehicle image dataset as well as the license
plate dataset, giving satisfactory performances.
| 2,015 |
A novel scheme for binarization of vehicle images using hierarchical
histogram equalization technique | 2,015 |
Biological data objects often have both of the following features: (i) they
are functions rather than single numbers or vectors, and (ii) they are
correlated due to phylogenetic relationships. In this paper we give a flexible
statistical model for such data, by combining assumptions from phylogenetics
with Gaussian processes. We describe its use as a nonparametric Bayesian prior
distribution, both for prediction (placing posterior distributions on ancestral
functions) and model selection (comparing rates of evolution across a
phylogeny, or identifying the most likely phylogenies consistent with the
observed data). Our work is integrative, extending the popular phylogenetic
Brownian Motion and Ornstein-Uhlenbeck models to functional data and Bayesian
inference, and extending Gaussian Process regression to phylogenies. We provide
a brief illustration of the application of our method.
| 2,012 |
Evolutionary Inference for Function-valued Traits: Gaussian Process
Regression on Phylogenies | 2,012 |
We introduce a theory of sequential causal inference in which learners in a
chain estimate a structural model from their upstream teacher and then pass
samples from the model to their downstream student. It extends the population
dynamics of genetic drift, recasting Kimura's selectively neutral theory as a
special case of a generalized drift process using structured populations with
memory. We examine the diffusion and fixation properties of several drift
processes and propose applications to learning, inference, and evolution. We
also demonstrate how the organization of drift process space controls fidelity,
facilitates innovations, and leads to information loss in sequential learning
with and without memory.
| 2,012 |
Structural Drift: The Population Dynamics of Sequential Learning | 2,012 |
We study the problem of estimating high-dimensional regression models
regularized by a structured sparsity-inducing penalty that encodes prior
structural information on either the input or output variables. We consider two
widely adopted types of penalties of this kind as motivating examples: (1) the
general overlapping-group-lasso penalty, generalized from the group-lasso
penalty; and (2) the graph-guided-fused-lasso penalty, generalized from the
fused-lasso penalty. For both types of penalties, due to their nonseparability
and nonsmoothness, developing an efficient optimization method remains a
challenging problem. In this paper we propose a general optimization approach,
the smoothing proximal gradient (SPG) method, which can solve structured sparse
regression problems with any smooth convex loss under a wide spectrum of
structured sparsity-inducing penalties. Our approach combines a smoothing
technique with an effective proximal gradient method. It achieves a convergence
rate significantly faster than the standard first-order methods, subgradient
methods, and is much more scalable than the most widely used interior-point
methods. The efficiency and scalability of our method are demonstrated on both
simulation experiments and real genetic data sets.
| 2,012 |
Smoothing proximal gradient method for general structured sparse
regression | 2,012 |
We consider the problem of sequential prediction and provide tools to study
the minimax value of the associated game. Classical statistical learning theory
provides several useful complexity measures to study learning with i.i.d. data.
Our proposed sequential complexities can be seen as extensions of these
measures to the sequential setting. The developed theory is shown to yield
precise learning guarantees for the problem of sequential prediction. In
particular, we show necessary and sufficient conditions for online learnability
in the setting of supervised learning. Several examples show the utility of our
framework: we can establish learnability without having to exhibit an explicit
online learning algorithm.
| 2,014 |
Online Learning via Sequential Complexities | 2,014 |
This companion paper complements the main DEFT'10 article describing the MARF
approach (arXiv:0905.1235) to the DEFT'10 NLP challenge (described at
http://www.groupes.polymtl.ca/taln2010/deft.php in French). This paper is aimed
to present the complete result sets of all the conducted experiments and their
settings in the resulting tables highlighting the approach and the best
results, but also showing the worse and the worst and their subsequent
analysis. This particular work focuses on application of the MARF's classical
and NLP pipelines to identification tasks within various francophone corpora to
identify decades when certain articles were published for the first track
(Piste 1) and place of origin of a publication (Piste 2), such as the journal
and location (France vs. Quebec). This is the sixth iteration of the release of
the results.
| 2,014 |
Complete Complementary Results Report of the MARF's NLP Approach to the
DEFT 2010 Competition | 2,014 |
One of the most visually demonstrable and straightforward uses of filtering
is in the field of Computer Vision. In this document we will try to outline the
issues encountered while designing and implementing a particle and kalman
filter based tracking system.
| 2,017 |
3D Visual Tracking with Particle and Kalman Filters | 2,017 |
The two parameter Poisson-Dirichlet Process (PDP), a generalisation of the
Dirichlet Process, is increasingly being used for probabilistic modelling in
discrete areas such as language technology, bioinformatics, and image analysis.
There is a rich literature about the PDP and its derivative distributions such
as the Chinese Restaurant Process (CRP). This article reviews some of the basic
theory and then the major results needed for Bayesian modelling of discrete
problems including details of priors, posteriors and computation.
The PDP allows one to build distributions over countable partitions. The PDP
has two other remarkable properties: first it is partially conjugate to itself,
which allows one to build hierarchies of PDPs, and second using a marginalised
relative the CRP, one gets fragmentation and clustering properties that lets
one layer partitions to build trees. This article presents the basic theory for
understanding the notion of partitions and distributions over them, the PDP and
the CRP, and the important properties of conjugacy, fragmentation and
clustering, as well as some key related properties such as consistency and
convergence. This article also presents a Bayesian interpretation of the
Poisson-Dirichlet process based on an improper and infinite dimensional
Dirichlet distribution. This means we can understand the process as just
another Dirichlet and thus all its sampling properties emerge naturally.
The theory of PDPs is usually presented for continuous distributions (more
generally referred to as non-atomic distributions), however, when applied to
discrete distributions its remarkable conjugacy property emerges. This context
and basic results are also presented, as well as techniques for computing the
second order Stirling numbers that occur in the posteriors for discrete
distributions.
| 2,012 |
A Bayesian View of the Poisson-Dirichlet Process | 2,012 |
Motivated by the unceasing interest in hidden Markov models (HMMs), this
paper re-examines hidden path inference in these models, using primarily a
risk-based framework. While the most common maximum a posteriori (MAP), or
Viterbi, path estimator and the minimum error, or Posterior Decoder (PD), have
long been around, other path estimators, or decoders, have been either only
hinted at or applied more recently and in dedicated applications generally
unfamiliar to the statistical learning community. Over a decade ago, however, a
family of algorithmically defined decoders aiming to hybridize the two standard
ones was proposed (Brushe et al., 1998). The present paper gives a careful
analysis of this hybridization approach, identifies several problems and issues
with it and other previously proposed approaches, and proposes practical
resolutions of those. Furthermore, simple modifications of the classical
criteria for hidden path recognition are shown to lead to a new class of
decoders. Dynamic programming algorithms to compute these decoders in the usual
forward-backward manner are presented. A particularly interesting subclass of
such estimators can be also viewed as hybrids of the MAP and PD estimators.
Similar to previously proposed MAP-PD hybrids, the new class is parameterized
by a small number of tunable parameters. Unlike their algorithmic predecessors,
the new risk-based decoders are more clearly interpretable, and, most
importantly, work "out of the box" in practice, which is demonstrated on some
real bioinformatics tasks and data. Some further generalizations and
applications are discussed in conclusion.
| 2,013 |
A generalized risk approach to path inference based on hidden Markov
models | 2,013 |
In this paper we present a new algorithm for learning oblique decision trees.
Most of the current decision tree algorithms rely on impurity measures to
assess the goodness of hyperplanes at each node while learning a decision tree
in a top-down fashion. These impurity measures do not properly capture the
geometric structures in the data. Motivated by this, our algorithm uses a
strategy to assess the hyperplanes in such a way that the geometric structure
in the data is taken into account. At each node of the decision tree, we find
the clustering hyperplanes for both the classes and use their angle bisectors
as the split rule at that node. We show through empirical studies that this
idea leads to small decision trees and better performance. We also present some
analysis to show that the angle bisectors of clustering hyperplanes that we use
as the split rules at each node, are solutions of an interesting optimization
problem and hence argue that this is a principled method of learning a decision
tree.
| 2,012 |
Geometric Decision Tree | 2,012 |
Margin theory provides one of the most popular explanations to the success of
\texttt{AdaBoost}, where the central point lies in the recognition that
\textit{margin} is the key for characterizing the performance of
\texttt{AdaBoost}. This theory has been very influential, e.g., it has been
used to argue that \texttt{AdaBoost} usually does not overfit since it tends to
enlarge the margin even after the training error reaches zero. Previously the
\textit{minimum margin bound} was established for \texttt{AdaBoost}, however,
\cite{Breiman1999} pointed out that maximizing the minimum margin does not
necessarily lead to a better generalization. Later, \cite{Reyzin:Schapire2006}
emphasized that the margin distribution rather than minimum margin is crucial
to the performance of \texttt{AdaBoost}. In this paper, we first present the
\textit{$k$th margin bound} and further study on its relationship to previous
work such as the minimum margin bound and Emargin bound. Then, we improve the
previous empirical Bernstein bounds
\citep{Maurer:Pontil2009,Audibert:Munos:Szepesvari2009}, and based on such
findings, we defend the margin-based explanation against Breiman's doubts by
proving a new generalization error bound that considers exactly the same
factors as \cite{Schapire:Freund:Bartlett:Lee1998} but is sharper than
\cite{Breiman1999}'s minimum margin bound. By incorporating factors such as
average margin and variance, we present a generalization error bound that is
heavily related to the whole margin distribution. We also provide margin
distribution bounds for generalization error of voting classifiers in finite
VC-dimension space.
| 2,013 |
On the Doubt about Margin Explanation of Boosting | 2,013 |
We establish an excess risk bound of O(H R_n^2 + R_n \sqrt{H L*}) for
empirical risk minimization with an H-smooth loss function and a hypothesis
class with Rademacher complexity R_n, where L* is the best risk achievable by
the hypothesis class. For typical hypothesis classes where R_n = \sqrt{R/n},
this translates to a learning rate of O(RH/n) in the separable (L*=0) case and
O(RH/n + \sqrt{L^* RH/n}) more generally. We also provide similar guarantees
for online and stochastic convex optimization with a smooth non-negative
objective.
| 2,012 |
Optimistic Rates for Learning with a Smooth Loss | 2,012 |
We consider the problem of energy-efficient point-to-point transmission of
delay-sensitive data (e.g. multimedia data) over a fading channel. Existing
research on this topic utilizes either physical-layer centric solutions, namely
power-control and adaptive modulation and coding (AMC), or system-level
solutions based on dynamic power management (DPM); however, there is currently
no rigorous and unified framework for simultaneously utilizing both
physical-layer centric and system-level techniques to achieve the minimum
possible energy consumption, under delay constraints, in the presence of
stochastic and a priori unknown traffic and channel conditions. In this report,
we propose such a framework. We formulate the stochastic optimization problem
as a Markov decision process (MDP) and solve it online using reinforcement
learning. The advantages of the proposed online method are that (i) it does not
require a priori knowledge of the traffic arrival and channel statistics to
determine the jointly optimal power-control, AMC, and DPM policies; (ii) it
exploits partial information about the system so that less information needs to
be learned than when using conventional reinforcement learning algorithms; and
(iii) it obviates the need for action exploration, which severely limits the
adaptation speed and run-time performance of conventional reinforcement
learning algorithms. Our results show that the proposed learning algorithms can
converge up to two orders of magnitude faster than a state-of-the-art learning
algorithm for physical layer power-control and up to three orders of magnitude
faster than conventional reinforcement learning algorithms.
| 2,013 |
Fast Reinforcement Learning for Energy-Efficient Wireless Communications | 2,013 |
To classify time series by nearest neighbors, we need to specify or learn one
or several distance measures. We consider variations of the Mahalanobis
distance measures which rely on the inverse covariance matrix of the data.
Unfortunately --- for time series data --- the covariance matrix has often low
rank. To alleviate this problem we can either use a pseudoinverse, covariance
shrinking or limit the matrix to its diagonal. We review these alternatives and
benchmark them against competitive methods such as the related Large Margin
Nearest Neighbor Classification (LMNN) and the Dynamic Time Warping (DTW)
distance. As we expected, we find that the DTW is superior, but the Mahalanobis
distance measures are one to two orders of magnitude faster. To get best
results with Mahalanobis distance measures, we recommend learning one distance
measure per class using either covariance shrinking or the diagonal approach.
| 2,012 |
Time Series Classification by Class-Specific Mahalanobis Distance
Measures | 2,012 |
We present a simple and fast geometric method for modeling data by a union of
affine subspaces. The method begins by forming a collection of local best-fit
affine subspaces, i.e., subspaces approximating the data in local
neighborhoods. The correct sizes of the local neighborhoods are determined
automatically by the Jones' $\beta_2$ numbers (we prove under certain geometric
conditions that our method finds the optimal local neighborhoods). The
collection of subspaces is further processed by a greedy selection procedure or
a spectral method to generate the final model. We discuss applications to
tracking-based motion segmentation and clustering of faces under different
illuminating conditions. We give extensive experimental evidence demonstrating
the state of the art accuracy and speed of the suggested algorithms on these
problems and also on synthetic hybrid linear data as well as the MNIST
handwritten digits data; and we demonstrate how to use our algorithms for fast
determination of the number of affine subspaces.
| 2,012 |
Hybrid Linear Modeling via Local Best-fit Flats | 2,012 |
A scattering vector is a local descriptor including multiscale and
multi-direction co-occurrence information. It is computed with a cascade of
wavelet decompositions and complex modulus. This scattering representation is
locally translation invariant and linearizes deformations. A supervised
classification algorithm is computed with a PCA model selection on scattering
vectors. State of the art results are obtained for handwritten digit
recognition and texture classification.
| 2,013 |
Classification with Scattering Operators | 2,013 |
We obtain a tight distribution-specific characterization of the sample
complexity of large-margin classification with L_2 regularization: We introduce
the \gamma-adapted-dimension, which is a simple function of the spectrum of a
distribution's covariance matrix, and show distribution-specific upper and
lower bounds on the sample complexity, both governed by the
\gamma-adapted-dimension of the source distribution. We conclude that this new
quantity tightly characterizes the true sample complexity of large-margin
classification. The bounds hold for a rich family of sub-Gaussian
distributions.
| 2,012 |
Tight Sample Complexity of Large-Margin Learning | 2,012 |
Many popular Bayesian nonparametric priors can be characterized in terms of
exchangeable species sampling sequences. However, in some applications,
exchangeability may not be appropriate. We introduce a {novel and
probabilistically coherent family of non-exchangeable species sampling
sequences characterized by a tractable predictive probability function with
weights driven by a sequence of independent Beta random variables. We compare
their theoretical clustering properties with those of the Dirichlet Process and
the two parameters Poisson-Dirichlet process. The proposed construction
provides a complete characterization of the joint process, differently from
existing work. We then propose the use of such process as prior distribution in
a hierarchical Bayes modeling framework, and we describe a Markov Chain Monte
Carlo sampler for posterior inference. We evaluate the performance of the prior
and the robustness of the resulting inference in a simulation study, providing
a comparison with popular Dirichlet Processes mixtures and Hidden Markov
Models. Finally, we develop an application to the detection of chromosomal
aberrations in breast cancer by leveraging array CGH data.
| 2,014 |
Generalized Species Sampling Priors with Latent Beta reinforcements | 2,014 |
We assume data sampled from a mixture of d-dimensional linear subspaces with
spherically symmetric distributions within each subspace and an additional
outlier component with spherically symmetric distribution within the ambient
space (for simplicity we may assume that all distributions are uniform on their
corresponding unit spheres). We also assume mixture weights for the different
components. We say that one of the underlying subspaces of the model is most
significant if its mixture weight is higher than the sum of the mixture weights
of all other subspaces. We study the recovery of the most significant subspace
by minimizing the lp-averaged distances of data points from d-dimensional
subspaces, where p>0. Unlike other lp minimization problems, this minimization
is non-convex for all p>0 and thus requires different methods for its analysis.
We show that if 0<p<=1, then for any fraction of outliers the most significant
subspace can be recovered by lp minimization with overwhelming probability
(which depends on the generating distribution and its parameters). We show that
when adding small noise around the underlying subspaces the most significant
subspace can be nearly recovered by lp minimization for any 0<p<=1 with an
error proportional to the noise level. On the other hand, if p>1 and there is
more than one underlying subspace, then with overwhelming probability the most
significant subspace cannot be recovered or nearly recovered. This last result
does not require spherically symmetric outliers.
| 2,014 |
lp-Recovery of the Most Significant Subspace among Multiple Subspaces
with Outliers | 2,014 |
We consider the problem of online linear regression on arbitrary
deterministic sequences when the ambient dimension d can be much larger than
the number of time rounds T. We introduce the notion of sparsity regret bound,
which is a deterministic online counterpart of recent risk bounds derived in
the stochastic setting under a sparsity scenario. We prove such regret bounds
for an online-learning algorithm called SeqSEW and based on exponential
weighting and data-driven truncation. In a second part we apply a
parameter-free version of this algorithm to the stochastic setting (regression
model with random design). This yields risk bounds of the same flavor as in
Dalalyan and Tsybakov (2011) but which solve two questions left open therein.
In particular our risk bounds are adaptive (up to a logarithmic factor) to the
unknown variance of the noise if the latter is Gaussian. We also address the
regression model with fixed design.
| 2,013 |
Sparsity regret bounds for individual sequences in online linear
regression | 2,013 |
This paper constructs translation invariant operators on L2(R^d), which are
Lipschitz continuous to the action of diffeomorphisms. A scattering propagator
is a path ordered product of non-linear and non-commuting operators, each of
which computes the modulus of a wavelet transform. A local integration defines
a windowed scattering transform, which is proved to be Lipschitz continuous to
the action of diffeomorphisms. As the window size increases, it converges to a
wavelet scattering transform which is translation invariant. Scattering
coefficients also provide representations of stationary processes. Expected
values depend upon high order moments and can discriminate processes having the
same power spectrum. Scattering operators are extended on L2 (G), where G is a
compact Lie group, and are invariant under the action of G. Combining a
scattering on L2(R^d) and on Ld (SO(d)) defines a translation and rotation
invariant scattering on L2(R^d).
| 2,012 |
Group Invariant Scattering | 2,012 |
This work is motivated by the problem of image mis-registration in remote
sensing and we are interested in determining the resulting loss in the accuracy
of pattern classification. A statistical formulation is given where we propose
to use data contamination to model and understand the phenomenon of image
mis-registration. This model is widely applicable to many other types of errors
as well, for example, measurement errors and gross errors etc. The impact of
data contamination on classification is studied under a statistical learning
theoretical framework. A closed-form asymptotic bound is established for the
resulting loss in classification accuracy, which is less than
$\epsilon/(1-\epsilon)$ for data contamination of an amount of $\epsilon$. Our
bound is sharper than similar bounds in the domain adaptation literature and,
unlike such bounds, it applies to classifiers with an infinite
Vapnik-Chervonekis (VC) dimension. Extensive simulations have been conducted on
both synthetic and real datasets under various types of data contamination,
including label flipping, feature swapping and the replacement of feature
values with data generated from a random source such as a Gaussian or Cauchy
distribution. Our simulation results show that the bound we derive is fairly
tight.
| 2,012 |
Classification under Data Contamination with Application to Remote
Sensing Image Mis-registration | 2,012 |
Targeting at sparse learning, we construct Banach spaces B of functions on an
input space X with the properties that (1) B possesses an l1 norm in the sense
that it is isometrically isomorphic to the Banach space of integrable functions
on X with respect to the counting measure; (2) point evaluations are continuous
linear functionals on B and are representable through a bilinear form with a
kernel function; (3) regularized learning schemes on B satisfy the linear
representer theorem. Examples of kernel functions admissible for the
construction of such spaces are given.
| 2,012 |
Reproducing Kernel Banach Spaces with the l1 Norm | 2,012 |
We consider a retailer selling a single product with limited on-hand
inventory over a finite selling season. Customer demand arrives according to a
Poisson process, the rate of which is influenced by a single action taken by
the retailer (such as price adjustment, sales commission, advertisement
intensity, etc.). The relationship between the action and the demand rate is
not known in advance. However, the retailer is able to learn the optimal action
"on the fly" as she maximizes her total expected revenue based on the observed
demand reactions.
Using the pricing problem as an example, we propose a dynamic
"learning-while-doing" algorithm that only involves function value estimation
to achieve a near-optimal performance. Our algorithm employs a series of
shrinking price intervals and iteratively tests prices within that interval
using a set of carefully chosen parameters. We prove that the convergence rate
of our algorithm is among the fastest of all possible algorithms in terms of
asymptotic "regret" (the relative loss comparing to the full information
optimal solution). Our result closes the performance gaps between parametric
and non-parametric learning and between a post-price mechanism and a
customer-bidding mechanism. Important managerial insight from this research is
that the values of information on both the parametric form of the demand
function as well as each customer's exact reservation price are less important
than prior literature suggests. Our results also suggest that firms would be
better off to perform dynamic learning and action concurrently rather than
sequentially.
| 2,013 |
Close the Gaps: A Learning-while-Doing Algorithm for a Class of
Single-Product Revenue Management Problems | 2,013 |
Boosting combines weak learners into a predictor with low empirical risk. Its
dual constructs a high entropy distribution upon which weak learners and
training labels are uncorrelated. This manuscript studies this primal-dual
relationship under a broad family of losses, including the exponential loss of
AdaBoost and the logistic loss, revealing:
- Weak learnability aids the whole loss family: for any {\epsilon}>0,
O(ln(1/{\epsilon})) iterations suffice to produce a predictor with empirical
risk {\epsilon}-close to the infimum;
- The circumstances granting the existence of an empirical risk minimizer may
be characterized in terms of the primal and dual problems, yielding a new proof
of the known rate O(ln(1/{\epsilon}));
- Arbitrary instances may be decomposed into the above two, granting rate
O(1/{\epsilon}), with a matching lower bound provided for the logistic loss.
| 2,012 |
A Primal-Dual Convergence Analysis of Boosting | 2,012 |
We reformulate minimalist grammars as partial functions on term algebras for
strings and trees. Using filler/role bindings and tensor product
representations, we construct homomorphisms for these data structures into
geometric vector spaces. We prove that the structure-building functions as well
as simple processors for minimalist languages can be realized by piecewise
linear operators in representation space. We also propose harmony, i.e. the
distance of an intermediate processing step from the final well-formed state in
representation space, as a measure of processing complexity. Finally, we
illustrate our findings by means of two particular arithmetic and fractal
representations.
| 2,012 |
Geometric representations for minimalist grammars | 2,012 |
Prediction markets are used in real life to predict outcomes of interest such
as presidential elections. This paper presents a mathematical theory of
artificial prediction markets for supervised learning of conditional
probability estimators. The artificial prediction market is a novel method for
fusing the prediction information of features or trained classifiers, where the
fusion result is the contract price on the possible outcomes. The market can be
trained online by updating the participants' budgets using training examples.
Inspired by the real prediction markets, the equations that govern the market
are derived from simple and reasonable assumptions. Efficient numerical
algorithms are presented for solving these equations. The obtained artificial
prediction market is shown to be a maximum likelihood estimator. It generalizes
linear aggregation, existent in boosting and random forest, as well as logistic
regression and some kernel methods. Furthermore, the market mechanism allows
the aggregation of specialized classifiers that participate only on specific
instances. Experimental comparisons show that the artificial prediction markets
often outperform random forest and implicit online learning on synthetic data
and real UCI datasets. Moreover, an extensive evaluation for pelvic and
abdominal lymph node detection in CT data shows that the prediction market
improves adaboost's detection rate from 79.6% to 81.2% at 3 false
positives/volume.
| 2,012 |
An Introduction to Artificial Prediction Markets for Classification | 2,012 |
Ordinal regression is commonly formulated as a multi-class problem with
ordinal constraints. The challenge of designing accurate classifiers for
ordinal regression generally increases with the number of classes involved, due
to the large number of labeled patterns that are needed. The availability of
ordinal class labels, however, is often costly to calibrate or difficult to
obtain. Unlabeled patterns, on the other hand, often exist in much greater
abundance and are freely available. To take benefits from the abundance of
unlabeled patterns, we present a novel transductive learning paradigm for
ordinal regression in this paper, namely Transductive Ordinal Regression (TOR).
The key challenge of the present study lies in the precise estimation of both
the ordinal class label of the unlabeled data and the decision functions of the
ordinal classes, simultaneously. The core elements of the proposed TOR include
an objective function that caters to several commonly used loss functions
casted in transductive settings, for general ordinal regression. A label
swapping scheme that facilitates a strictly monotonic decrease in the objective
function value is also introduced. Extensive numerical studies on commonly used
benchmark datasets including the real world sentiment prediction problem are
then presented to showcase the characteristics and efficacies of the proposed
transductive ordinal regression. Further, comparisons to recent
state-of-the-art ordinal regression methods demonstrate the introduced
transductive learning paradigm for ordinal regression led to the robust and
improved performance.
| 2,012 |
Transductive Ordinal Regression | 2,012 |
Feature selection with specific multivariate performance measures is the key
to the success of many applications, such as image retrieval and text
classification. The existing feature selection methods are usually designed for
classification error. In this paper, we propose a generalized sparse
regularizer. Based on the proposed regularizer, we present a unified feature
selection framework for general loss functions. In particular, we study the
novel feature selection paradigm by optimizing multivariate performance
measures. The resultant formulation is a challenging problem for
high-dimensional data. Hence, a two-layer cutting plane algorithm is proposed
to solve this problem, and the convergence is presented. In addition, we adapt
the proposed method to optimize multivariate measures for multiple instance
learning problems. The analyses by comparing with the state-of-the-art feature
selection methods show that the proposed method is superior to others.
Extensive experiments on large-scale and high-dimensional real world datasets
show that the proposed method outperforms $l_1$-SVM and SVM-RFE when choosing a
small subset of features, and achieves significantly improved performances over
SVM$^{perf}$ in terms of $F_1$-score.
| 2,013 |
A Feature Selection Method for Multivariate Performance Measures | 2,013 |
In the 21st century, Aerial and satellite images are information rich. They
are also complex to analyze. For GIS systems, many features require fast and
reliable extraction of open space area from high resolution satellite imagery.
In this paper we will study efficient and reliable automatic extraction
algorithm to find out the open space area from the high resolution urban
satellite imagery. This automatic extraction algorithm uses some filters and
segmentations and grouping is applying on satellite images. And the result
images may use to calculate the total available open space area and the built
up area. It may also use to compare the difference between present and past
open space area using historical urban satellite images of that same projection
| 2,022 |
Automatic Extraction of Open Space Area from High Resolution Urban
Satellite Imagery | 2,022 |
In many practical applications of clustering, the objects to be clustered
evolve over time, and a clustering result is desired at each time step. In such
applications, evolutionary clustering typically outperforms traditional static
clustering by producing clustering results that reflect long-term trends while
being robust to short-term variations. Several evolutionary clustering
algorithms have recently been proposed, often by adding a temporal smoothness
penalty to the cost function of a static clustering method. In this paper, we
introduce a different approach to evolutionary clustering by accurately
tracking the time-varying proximities between objects followed by static
clustering. We present an evolutionary clustering framework that adaptively
estimates the optimal smoothing parameter using shrinkage estimation, a
statistical approach that improves a naive estimate using additional
information. The proposed framework can be used to extend a variety of static
clustering algorithms, including hierarchical, k-means, and spectral
clustering, into evolutionary clustering algorithms. Experiments on synthetic
and real data sets indicate that the proposed framework outperforms static
clustering and existing evolutionary clustering algorithms in many scenarios.
| 2,013 |
Adaptive Evolutionary Clustering | 2,013 |
With inspiration from Random Forests (RF) in the context of classification, a
new clustering ensemble method---Cluster Forests (CF) is proposed.
Geometrically, CF randomly probes a high-dimensional data cloud to obtain "good
local clusterings" and then aggregates via spectral clustering to obtain
cluster assignments for the whole dataset. The search for good local
clusterings is guided by a cluster quality measure kappa. CF progressively
improves each local clustering in a fashion that resembles the tree growth in
RF. Empirical studies on several real-world datasets under two different
performance metrics show that CF compares favorably to its competitors.
Theoretical analysis reveals that the kappa measure makes it possible to grow
the local clustering in a desirable way---it is "noise-resistant". A
closed-form expression is obtained for the mis-clustering rate of spectral
clustering under a perturbation model, which yields new insights into some
aspects of spectral clustering.
| 2,013 |
Cluster Forests | 2,013 |
Gabor filters play an important role in many application areas for the
enhancement of various types of images and the extraction of Gabor features.
For the purpose of enhancing curved structures in noisy images, we introduce
curved Gabor filters which locally adapt their shape to the direction of flow.
These curved Gabor filters enable the choice of filter parameters which
increase the smoothing power without creating artifacts in the enhanced image.
In this paper, curved Gabor filters are applied to the curved ridge and valley
structure of low-quality fingerprint images. First, we combine two orientation
field estimation methods in order to obtain a more robust estimation for very
noisy images. Next, curved regions are constructed by following the respective
local orientation and they are used for estimating the local ridge frequency.
Lastly, curved Gabor filters are defined based on curved regions and they are
applied for the enhancement of low-quality fingerprint images. Experimental
results on the FVC2004 databases show improvements of this approach in
comparison to state-of-the-art enhancement methods.
| 2,014 |
Curved Gabor Filters for Fingerprint Image Enhancement | 2,014 |
The success of many machine learning and pattern recognition methods relies
heavily upon the identification of an appropriate distance metric on the input
data. It is often beneficial to learn such a metric from the input training
data, instead of using a default one such as the Euclidean distance. In this
work, we propose a boosting-based technique, termed BoostMetric, for learning a
quadratic Mahalanobis distance metric. Learning a valid Mahalanobis distance
metric requires enforcing the constraint that the matrix parameter to the
metric remains positive definite. Semidefinite programming is often used to
enforce this constraint, but does not scale well and easy to implement.
BoostMetric is instead based on the observation that any positive semidefinite
matrix can be decomposed into a linear combination of trace-one rank-one
matrices. BoostMetric thus uses rank-one positive semidefinite matrices as weak
learners within an efficient and scalable boosting-based learning process. The
resulting methods are easy to implement, efficient, and can accommodate various
types of constraints. We extend traditional boosting algorithms in that its
weak learner is a positive semidefinite matrix with trace and rank being one
rather than a classifier or regressor. Experiments on various datasets
demonstrate that the proposed algorithms compare favorably to those
state-of-the-art methods in terms of classification accuracy and running time.
| 2,012 |
Positive Semidefinite Metric Learning Using Boosting-like Algorithms | 2,012 |
This paper considers the problem of clustering a partially observed
unweighted graph---i.e., one where for some node pairs we know there is an edge
between them, for some others we know there is no edge, and for the remaining
we do not know whether or not there is an edge. We want to organize the nodes
into disjoint clusters so that there is relatively dense (observed)
connectivity within clusters, and sparse across clusters.
We take a novel yet natural approach to this problem, by focusing on finding
the clustering that minimizes the number of "disagreements"---i.e., the sum of
the number of (observed) missing edges within clusters, and (observed) present
edges across clusters. Our algorithm uses convex optimization; its basis is a
reduction of disagreement minimization to the problem of recovering an
(unknown) low-rank matrix and an (unknown) sparse matrix from their partially
observed sum. We evaluate the performance of our algorithm on the classical
Planted Partition/Stochastic Block Model. Our main theorem provides sufficient
conditions for the success of our algorithm as a function of the minimum
cluster size, edge density and observation probability; in particular, the
results characterize the tradeoff between the observation probability and the
edge density gap. When there are a constant number of clusters of equal size,
our results are optimal up to logarithmic factors.
| 2,014 |
Clustering Partially Observed Graphs via Convex Optimization | 2,014 |
We present a new application and covering number bound for the framework of
"Machine Learning with Operational Costs (MLOC)," which is an exploratory form
of decision theory. The MLOC framework incorporates knowledge about how a
predictive model will be used for a subsequent task, thus combining machine
learning with the decision that is made afterwards. In this work, we use the
MLOC framework to study a problem that has implications for power grid
reliability and maintenance, called the Machine Learning and Traveling
Repairman Problem ML&TRP. The goal of the ML&TRP is to determine a route for a
"repair crew," which repairs nodes on a graph. The repair crew aims to minimize
the cost of failures at the nodes, but as in many real situations, the failure
probabilities are not known and must be estimated. The MLOC framework allows us
to understand how this uncertainty influences the repair route. We also present
new covering number generalization bounds for the MLOC framework.
| 2,014 |
On Combining Machine Learning with Decision Making | 2,014 |
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