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0 | 0 | Learning from compressed observations | The problem of statistical learning is to construct a predictor of a random
variable $Y$ as a function of a related random variable $X$ on the basis of an
i.i.d. training sample from the joint distribution of $(X,Y)$. Allowable
predictors are drawn from some specified class, and the goal is to approach
asymptotically the performance (expected loss) of the best predictor in the
class. We consider the setting in which one has perfect observation of the
$X$-part of the sample, while the $Y$-part has to be communicated at some
finite bit rate. The encoding of the $Y$-values is allowed to depend on the
$X$-values. Under suitable regularity conditions on the admissible predictors,
the underlying family of probability distributions and the loss function, we
give an information-theoretic characterization of achievable predictor
performance in terms of conditional distortion-rate functions. The ideas are
illustrated on the example of nonparametric regression in Gaussian noise.
| Learning from compressed observations The problem of statistical learning is to construct a predictor of a random
variable $Y$ as a function of a related random variable $X$ on the basis of an
i.i.d. training sample from the joint distribution of $(X,Y)$. Allowable
predictors are drawn from some specified class, and the goal is to approach
asymptotically the performance (expected loss) of the best predictor in the
class. We consider the setting in which one has perfect observation of the
$X$-part of the sample, while the $Y$-part has to be communicated at some
finite bit rate. The encoding of the $Y$-values is allowed to depend on the
$X$-values. Under suitable regularity conditions on the admissible predictors,
the underlying family of probability distributions and the loss function, we
give an information-theoretic characterization of achievable predictor
performance in terms of conditional distortion-rate functions. The ideas are
illustrated on the example of nonparametric regression in Gaussian noise.
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] |
1 | 1 | Sensor Networks with Random Links: Topology Design for Distributed
Consensus | In a sensor network, in practice, the communication among sensors is subject
to:(1) errors or failures at random times; (3) costs; and(2) constraints since
sensors and networks operate under scarce resources, such as power, data rate,
or communication. The signal-to-noise ratio (SNR) is usually a main factor in
determining the probability of error (or of communication failure) in a link.
These probabilities are then a proxy for the SNR under which the links operate.
The paper studies the problem of designing the topology, i.e., assigning the
probabilities of reliable communication among sensors (or of link failures) to
maximize the rate of convergence of average consensus, when the link
communication costs are taken into account, and there is an overall
communication budget constraint. To consider this problem, we address a number
of preliminary issues: (1) model the network as a random topology; (2)
establish necessary and sufficient conditions for mean square sense (mss) and
almost sure (a.s.) convergence of average consensus when network links fail;
and, in particular, (3) show that a necessary and sufficient condition for both
mss and a.s. convergence is for the algebraic connectivity of the mean graph
describing the network topology to be strictly positive. With these results, we
formulate topology design, subject to random link failures and to a
communication cost constraint, as a constrained convex optimization problem to
which we apply semidefinite programming techniques. We show by an extensive
numerical study that the optimal design improves significantly the convergence
speed of the consensus algorithm and can achieve the asymptotic performance of
a non-random network at a fraction of the communication cost.
| Sensor Networks with Random Links: Topology Design for Distributed
Consensus In a sensor network, in practice, the communication among sensors is subject
to:(1) errors or failures at random times; (3) costs; and(2) constraints since
sensors and networks operate under scarce resources, such as power, data rate,
or communication. The signal-to-noise ratio (SNR) is usually a main factor in
determining the probability of error (or of communication failure) in a link.
These probabilities are then a proxy for the SNR under which the links operate.
The paper studies the problem of designing the topology, i.e., assigning the
probabilities of reliable communication among sensors (or of link failures) to
maximize the rate of convergence of average consensus, when the link
communication costs are taken into account, and there is an overall
communication budget constraint. To consider this problem, we address a number
of preliminary issues: (1) model the network as a random topology; (2)
establish necessary and sufficient conditions for mean square sense (mss) and
almost sure (a.s.) convergence of average consensus when network links fail;
and, in particular, (3) show that a necessary and sufficient condition for both
mss and a.s. convergence is for the algebraic connectivity of the mean graph
describing the network topology to be strictly positive. With these results, we
formulate topology design, subject to random link failures and to a
communication cost constraint, as a constrained convex optimization problem to
which we apply semidefinite programming techniques. We show by an extensive
numerical study that the optimal design improves significantly the convergence
speed of the consensus algorithm and can achieve the asymptotic performance of
a non-random network at a fraction of the communication cost.
| [
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] |
2 | 2 | The on-line shortest path problem under partial monitoring | The on-line shortest path problem is considered under various models of
partial monitoring. Given a weighted directed acyclic graph whose edge weights
can change in an arbitrary (adversarial) way, a decision maker has to choose in
each round of a game a path between two distinguished vertices such that the
loss of the chosen path (defined as the sum of the weights of its composing
edges) be as small as possible. In a setting generalizing the multi-armed
bandit problem, after choosing a path, the decision maker learns only the
weights of those edges that belong to the chosen path. For this problem, an
algorithm is given whose average cumulative loss in n rounds exceeds that of
the best path, matched off-line to the entire sequence of the edge weights, by
a quantity that is proportional to 1/\sqrt{n} and depends only polynomially on
the number of edges of the graph. The algorithm can be implemented with linear
complexity in the number of rounds n and in the number of edges. An extension
to the so-called label efficient setting is also given, in which the decision
maker is informed about the weights of the edges corresponding to the chosen
path at a total of m << n time instances. Another extension is shown where the
decision maker competes against a time-varying path, a generalization of the
problem of tracking the best expert. A version of the multi-armed bandit
setting for shortest path is also discussed where the decision maker learns
only the total weight of the chosen path but not the weights of the individual
edges on the path. Applications to routing in packet switched networks along
with simulation results are also presented.
| The on-line shortest path problem under partial monitoring The on-line shortest path problem is considered under various models of
partial monitoring. Given a weighted directed acyclic graph whose edge weights
can change in an arbitrary (adversarial) way, a decision maker has to choose in
each round of a game a path between two distinguished vertices such that the
loss of the chosen path (defined as the sum of the weights of its composing
edges) be as small as possible. In a setting generalizing the multi-armed
bandit problem, after choosing a path, the decision maker learns only the
weights of those edges that belong to the chosen path. For this problem, an
algorithm is given whose average cumulative loss in n rounds exceeds that of
the best path, matched off-line to the entire sequence of the edge weights, by
a quantity that is proportional to 1/\sqrt{n} and depends only polynomially on
the number of edges of the graph. The algorithm can be implemented with linear
complexity in the number of rounds n and in the number of edges. An extension
to the so-called label efficient setting is also given, in which the decision
maker is informed about the weights of the edges corresponding to the chosen
path at a total of m << n time instances. Another extension is shown where the
decision maker competes against a time-varying path, a generalization of the
problem of tracking the best expert. A version of the multi-armed bandit
setting for shortest path is also discussed where the decision maker learns
only the total weight of the chosen path but not the weights of the individual
edges on the path. Applications to routing in packet switched networks along
with simulation results are also presented.
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] |
3 | 3 | A neural network approach to ordinal regression | Ordinal regression is an important type of learning, which has properties of
both classification and regression. Here we describe a simple and effective
approach to adapt a traditional neural network to learn ordinal categories. Our
approach is a generalization of the perceptron method for ordinal regression.
On several benchmark datasets, our method (NNRank) outperforms a neural network
classification method. Compared with the ordinal regression methods using
Gaussian processes and support vector machines, NNRank achieves comparable
performance. Moreover, NNRank has the advantages of traditional neural
networks: learning in both online and batch modes, handling very large training
datasets, and making rapid predictions. These features make NNRank a useful and
complementary tool for large-scale data processing tasks such as information
retrieval, web page ranking, collaborative filtering, and protein ranking in
Bioinformatics.
| A neural network approach to ordinal regression Ordinal regression is an important type of learning, which has properties of
both classification and regression. Here we describe a simple and effective
approach to adapt a traditional neural network to learn ordinal categories. Our
approach is a generalization of the perceptron method for ordinal regression.
On several benchmark datasets, our method (NNRank) outperforms a neural network
classification method. Compared with the ordinal regression methods using
Gaussian processes and support vector machines, NNRank achieves comparable
performance. Moreover, NNRank has the advantages of traditional neural
networks: learning in both online and batch modes, handling very large training
datasets, and making rapid predictions. These features make NNRank a useful and
complementary tool for large-scale data processing tasks such as information
retrieval, web page ranking, collaborative filtering, and protein ranking in
Bioinformatics.
| [
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] |
4 | 4 | Parametric Learning and Monte Carlo Optimization | This paper uncovers and explores the close relationship between Monte Carlo
Optimization of a parametrized integral (MCO), Parametric machine-Learning
(PL), and `blackbox' or `oracle'-based optimization (BO). We make four
contributions. First, we prove that MCO is mathematically identical to a broad
class of PL problems. This identity potentially provides a new application
domain for all broadly applicable PL techniques: MCO. Second, we introduce
immediate sampling, a new version of the Probability Collectives (PC) algorithm
for blackbox optimization. Immediate sampling transforms the original BO
problem into an MCO problem. Accordingly, by combining these first two
contributions, we can apply all PL techniques to BO. In our third contribution
we validate this way of improving BO by demonstrating that cross-validation and
bagging improve immediate sampling. Finally, conventional MC and MCO procedures
ignore the relationship between the sample point locations and the associated
values of the integrand; only the values of the integrand at those locations
are considered. We demonstrate that one can exploit the sample location
information using PL techniques, for example by forming a fit of the sample
locations to the associated values of the integrand. This provides an
additional way to apply PL techniques to improve MCO.
| Parametric Learning and Monte Carlo Optimization This paper uncovers and explores the close relationship between Monte Carlo
Optimization of a parametrized integral (MCO), Parametric machine-Learning
(PL), and `blackbox' or `oracle'-based optimization (BO). We make four
contributions. First, we prove that MCO is mathematically identical to a broad
class of PL problems. This identity potentially provides a new application
domain for all broadly applicable PL techniques: MCO. Second, we introduce
immediate sampling, a new version of the Probability Collectives (PC) algorithm
for blackbox optimization. Immediate sampling transforms the original BO
problem into an MCO problem. Accordingly, by combining these first two
contributions, we can apply all PL techniques to BO. In our third contribution
we validate this way of improving BO by demonstrating that cross-validation and
bagging improve immediate sampling. Finally, conventional MC and MCO procedures
ignore the relationship between the sample point locations and the associated
values of the integrand; only the values of the integrand at those locations
are considered. We demonstrate that one can exploit the sample location
information using PL techniques, for example by forming a fit of the sample
locations to the associated values of the integrand. This provides an
additional way to apply PL techniques to improve MCO.
| [
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] |
5 | 5 | Preconditioned Temporal Difference Learning | This paper has been withdrawn by the author. This draft is withdrawn for its
poor quality in english, unfortunately produced by the author when he was just
starting his science route. Look at the ICML version instead:
http://icml2008.cs.helsinki.fi/papers/111.pdf
| Preconditioned Temporal Difference Learning This paper has been withdrawn by the author. This draft is withdrawn for its
poor quality in english, unfortunately produced by the author when he was just
starting his science route. Look at the ICML version instead:
http://icml2008.cs.helsinki.fi/papers/111.pdf
| [
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] |
6 | 6 | A Note on the Inapproximability of Correlation Clustering | We consider inapproximability of the correlation clustering problem defined
as follows: Given a graph $G = (V,E)$ where each edge is labeled either "+"
(similar) or "-" (dissimilar), correlation clustering seeks to partition the
vertices into clusters so that the number of pairs correctly (resp.
incorrectly) classified with respect to the labels is maximized (resp.
minimized). The two complementary problems are called MaxAgree and MinDisagree,
respectively, and have been studied on complete graphs, where every edge is
labeled, and general graphs, where some edge might not have been labeled.
Natural edge-weighted versions of both problems have been studied as well. Let
S-MaxAgree denote the weighted problem where all weights are taken from set S,
we show that S-MaxAgree with weights bounded by $O(|V|^{1/2-\delta})$
essentially belongs to the same hardness class in the following sense: if there
is a polynomial time algorithm that approximates S-MaxAgree within a factor of
$\lambda = O(\log{|V|})$ with high probability, then for any choice of S',
S'-MaxAgree can be approximated in polynomial time within a factor of $(\lambda
+ \epsilon)$, where $\epsilon > 0$ can be arbitrarily small, with high
probability. A similar statement also holds for $S-MinDisagree. This result
implies it is hard (assuming $NP \neq RP$) to approximate unweighted MaxAgree
within a factor of $80/79-\epsilon$, improving upon a previous known factor of
$116/115-\epsilon$ by Charikar et. al. \cite{Chari05}.
| A Note on the Inapproximability of Correlation Clustering We consider inapproximability of the correlation clustering problem defined
as follows: Given a graph $G = (V,E)$ where each edge is labeled either "+"
(similar) or "-" (dissimilar), correlation clustering seeks to partition the
vertices into clusters so that the number of pairs correctly (resp.
incorrectly) classified with respect to the labels is maximized (resp.
minimized). The two complementary problems are called MaxAgree and MinDisagree,
respectively, and have been studied on complete graphs, where every edge is
labeled, and general graphs, where some edge might not have been labeled.
Natural edge-weighted versions of both problems have been studied as well. Let
S-MaxAgree denote the weighted problem where all weights are taken from set S,
we show that S-MaxAgree with weights bounded by $O(|V|^{1/2-\delta})$
essentially belongs to the same hardness class in the following sense: if there
is a polynomial time algorithm that approximates S-MaxAgree within a factor of
$\lambda = O(\log{|V|})$ with high probability, then for any choice of S',
S'-MaxAgree can be approximated in polynomial time within a factor of $(\lambda
+ \epsilon)$, where $\epsilon > 0$ can be arbitrarily small, with high
probability. A similar statement also holds for $S-MinDisagree. This result
implies it is hard (assuming $NP \neq RP$) to approximate unweighted MaxAgree
within a factor of $80/79-\epsilon$, improving upon a previous known factor of
$116/115-\epsilon$ by Charikar et. al. \cite{Chari05}.
| [
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] |
7 | 7 | Joint universal lossy coding and identification of stationary mixing
sources | The problem of joint universal source coding and modeling, treated in the
context of lossless codes by Rissanen, was recently generalized to fixed-rate
lossy coding of finitely parametrized continuous-alphabet i.i.d. sources. We
extend these results to variable-rate lossy block coding of stationary ergodic
sources and show that, for bounded metric distortion measures, any finitely
parametrized family of stationary sources satisfying suitable mixing,
smoothness and Vapnik-Chervonenkis learnability conditions admits universal
schemes for joint lossy source coding and identification. We also give several
explicit examples of parametric sources satisfying the regularity conditions.
| Joint universal lossy coding and identification of stationary mixing
sources The problem of joint universal source coding and modeling, treated in the
context of lossless codes by Rissanen, was recently generalized to fixed-rate
lossy coding of finitely parametrized continuous-alphabet i.i.d. sources. We
extend these results to variable-rate lossy block coding of stationary ergodic
sources and show that, for bounded metric distortion measures, any finitely
parametrized family of stationary sources satisfying suitable mixing,
smoothness and Vapnik-Chervonenkis learnability conditions admits universal
schemes for joint lossy source coding and identification. We also give several
explicit examples of parametric sources satisfying the regularity conditions.
| [
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] |
8 | 8 | Supervised Feature Selection via Dependence Estimation | We introduce a framework for filtering features that employs the
Hilbert-Schmidt Independence Criterion (HSIC) as a measure of dependence
between the features and the labels. The key idea is that good features should
maximise such dependence. Feature selection for various supervised learning
problems (including classification and regression) is unified under this
framework, and the solutions can be approximated using a backward-elimination
algorithm. We demonstrate the usefulness of our method on both artificial and
real world datasets.
| Supervised Feature Selection via Dependence Estimation We introduce a framework for filtering features that employs the
Hilbert-Schmidt Independence Criterion (HSIC) as a measure of dependence
between the features and the labels. The key idea is that good features should
maximise such dependence. Feature selection for various supervised learning
problems (including classification and regression) is unified under this
framework, and the solutions can be approximated using a backward-elimination
algorithm. We demonstrate the usefulness of our method on both artificial and
real world datasets.
| [
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] |
9 | 9 | Equivalence of LP Relaxation and Max-Product for Weighted Matching in
General Graphs | Max-product belief propagation is a local, iterative algorithm to find the
mode/MAP estimate of a probability distribution. While it has been successfully
employed in a wide variety of applications, there are relatively few
theoretical guarantees of convergence and correctness for general loopy graphs
that may have many short cycles. Of these, even fewer provide exact ``necessary
and sufficient'' characterizations.
In this paper we investigate the problem of using max-product to find the
maximum weight matching in an arbitrary graph with edge weights. This is done
by first constructing a probability distribution whose mode corresponds to the
optimal matching, and then running max-product. Weighted matching can also be
posed as an integer program, for which there is an LP relaxation. This
relaxation is not always tight. In this paper we show that \begin{enumerate}
\item If the LP relaxation is tight, then max-product always converges, and
that too to the correct answer. \item If the LP relaxation is loose, then
max-product does not converge. \end{enumerate} This provides an exact,
data-dependent characterization of max-product performance, and a precise
connection to LP relaxation, which is a well-studied optimization technique.
Also, since LP relaxation is known to be tight for bipartite graphs, our
results generalize other recent results on using max-product to find weighted
matchings in bipartite graphs.
| Equivalence of LP Relaxation and Max-Product for Weighted Matching in
General Graphs Max-product belief propagation is a local, iterative algorithm to find the
mode/MAP estimate of a probability distribution. While it has been successfully
employed in a wide variety of applications, there are relatively few
theoretical guarantees of convergence and correctness for general loopy graphs
that may have many short cycles. Of these, even fewer provide exact ``necessary
and sufficient'' characterizations.
In this paper we investigate the problem of using max-product to find the
maximum weight matching in an arbitrary graph with edge weights. This is done
by first constructing a probability distribution whose mode corresponds to the
optimal matching, and then running max-product. Weighted matching can also be
posed as an integer program, for which there is an LP relaxation. This
relaxation is not always tight. In this paper we show that \begin{enumerate}
\item If the LP relaxation is tight, then max-product always converges, and
that too to the correct answer. \item If the LP relaxation is loose, then
max-product does not converge. \end{enumerate} This provides an exact,
data-dependent characterization of max-product performance, and a precise
connection to LP relaxation, which is a well-studied optimization technique.
Also, since LP relaxation is known to be tight for bipartite graphs, our
results generalize other recent results on using max-product to find weighted
matchings in bipartite graphs.
| [
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] |
10 | 10 | HMM Speaker Identification Using Linear and Non-linear Merging
Techniques | Speaker identification is a powerful, non-invasive and in-expensive biometric
technique. The recognition accuracy, however, deteriorates when noise levels
affect a specific band of frequency. In this paper, we present a sub-band based
speaker identification that intends to improve the live testing performance.
Each frequency sub-band is processed and classified independently. We also
compare the linear and non-linear merging techniques for the sub-bands
recognizer. Support vector machines and Gaussian Mixture models are the
non-linear merging techniques that are investigated. Results showed that the
sub-band based method used with linear merging techniques enormously improved
the performance of the speaker identification over the performance of wide-band
recognizers when tested live. A live testing improvement of 9.78% was achieved
| HMM Speaker Identification Using Linear and Non-linear Merging
Techniques Speaker identification is a powerful, non-invasive and in-expensive biometric
technique. The recognition accuracy, however, deteriorates when noise levels
affect a specific band of frequency. In this paper, we present a sub-band based
speaker identification that intends to improve the live testing performance.
Each frequency sub-band is processed and classified independently. We also
compare the linear and non-linear merging techniques for the sub-bands
recognizer. Support vector machines and Gaussian Mixture models are the
non-linear merging techniques that are investigated. Results showed that the
sub-band based method used with linear merging techniques enormously improved
the performance of the speaker identification over the performance of wide-band
recognizers when tested live. A live testing improvement of 9.78% was achieved
| [
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] |
11 | 11 | Statistical Mechanics of Nonlinear On-line Learning for Ensemble
Teachers | We analyze the generalization performance of a student in a model composed of
nonlinear perceptrons: a true teacher, ensemble teachers, and the student. We
calculate the generalization error of the student analytically or numerically
using statistical mechanics in the framework of on-line learning. We treat two
well-known learning rules: Hebbian learning and perceptron learning. As a
result, it is proven that the nonlinear model shows qualitatively different
behaviors from the linear model. Moreover, it is clarified that Hebbian
learning and perceptron learning show qualitatively different behaviors from
each other. In Hebbian learning, we can analytically obtain the solutions. In
this case, the generalization error monotonically decreases. The steady value
of the generalization error is independent of the learning rate. The larger the
number of teachers is and the more variety the ensemble teachers have, the
smaller the generalization error is. In perceptron learning, we have to
numerically obtain the solutions. In this case, the dynamical behaviors of the
generalization error are non-monotonic. The smaller the learning rate is, the
larger the number of teachers is; and the more variety the ensemble teachers
have, the smaller the minimum value of the generalization error is.
| Statistical Mechanics of Nonlinear On-line Learning for Ensemble
Teachers We analyze the generalization performance of a student in a model composed of
nonlinear perceptrons: a true teacher, ensemble teachers, and the student. We
calculate the generalization error of the student analytically or numerically
using statistical mechanics in the framework of on-line learning. We treat two
well-known learning rules: Hebbian learning and perceptron learning. As a
result, it is proven that the nonlinear model shows qualitatively different
behaviors from the linear model. Moreover, it is clarified that Hebbian
learning and perceptron learning show qualitatively different behaviors from
each other. In Hebbian learning, we can analytically obtain the solutions. In
this case, the generalization error monotonically decreases. The steady value
of the generalization error is independent of the learning rate. The larger the
number of teachers is and the more variety the ensemble teachers have, the
smaller the generalization error is. In perceptron learning, we have to
numerically obtain the solutions. In this case, the dynamical behaviors of the
generalization error are non-monotonic. The smaller the learning rate is, the
larger the number of teachers is; and the more variety the ensemble teachers
have, the smaller the minimum value of the generalization error is.
| [
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] |
12 | 12 | On the monotonization of the training set | We consider the problem of minimal correction of the training set to make it
consistent with monotonic constraints. This problem arises during analysis of
data sets via techniques that require monotone data. We show that this problem
is NP-hard in general and is equivalent to finding a maximal independent set in
special orgraphs. Practically important cases of that problem considered in
detail. These are the cases when a partial order given on the replies set is a
total order or has a dimension 2. We show that the second case can be reduced
to maximization of a quadratic convex function on a convex set. For this case
we construct an approximate polynomial algorithm based on convex optimization.
| On the monotonization of the training set We consider the problem of minimal correction of the training set to make it
consistent with monotonic constraints. This problem arises during analysis of
data sets via techniques that require monotone data. We show that this problem
is NP-hard in general and is equivalent to finding a maximal independent set in
special orgraphs. Practically important cases of that problem considered in
detail. These are the cases when a partial order given on the replies set is a
total order or has a dimension 2. We show that the second case can be reduced
to maximization of a quadratic convex function on a convex set. For this case
we construct an approximate polynomial algorithm based on convex optimization.
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] |
13 | 13 | Mixed membership stochastic blockmodels | Observations consisting of measurements on relationships for pairs of objects
arise in many settings, such as protein interaction and gene regulatory
networks, collections of author-recipient email, and social networks. Analyzing
such data with probabilisic models can be delicate because the simple
exchangeability assumptions underlying many boilerplate models no longer hold.
In this paper, we describe a latent variable model of such data called the
mixed membership stochastic blockmodel. This model extends blockmodels for
relational data to ones which capture mixed membership latent relational
structure, thus providing an object-specific low-dimensional representation. We
develop a general variational inference algorithm for fast approximate
posterior inference. We explore applications to social and protein interaction
networks.
| Mixed membership stochastic blockmodels Observations consisting of measurements on relationships for pairs of objects
arise in many settings, such as protein interaction and gene regulatory
networks, collections of author-recipient email, and social networks. Analyzing
such data with probabilisic models can be delicate because the simple
exchangeability assumptions underlying many boilerplate models no longer hold.
In this paper, we describe a latent variable model of such data called the
mixed membership stochastic blockmodel. This model extends blockmodels for
relational data to ones which capture mixed membership latent relational
structure, thus providing an object-specific low-dimensional representation. We
develop a general variational inference algorithm for fast approximate
posterior inference. We explore applications to social and protein interaction
networks.
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] |
14 | 14 | Loop corrections for message passing algorithms in continuous variable
models | In this paper we derive the equations for Loop Corrected Belief Propagation
on a continuous variable Gaussian model. Using the exactness of the averages
for belief propagation for Gaussian models, a different way of obtaining the
covariances is found, based on Belief Propagation on cavity graphs. We discuss
the relation of this loop correction algorithm to Expectation Propagation
algorithms for the case in which the model is no longer Gaussian, but slightly
perturbed by nonlinear terms.
| Loop corrections for message passing algorithms in continuous variable
models In this paper we derive the equations for Loop Corrected Belief Propagation
on a continuous variable Gaussian model. Using the exactness of the averages
for belief propagation for Gaussian models, a different way of obtaining the
covariances is found, based on Belief Propagation on cavity graphs. We discuss
the relation of this loop correction algorithm to Expectation Propagation
algorithms for the case in which the model is no longer Gaussian, but slightly
perturbed by nonlinear terms.
| [
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] |
15 | 15 | A Novel Model of Working Set Selection for SMO Decomposition Methods | In the process of training Support Vector Machines (SVMs) by decomposition
methods, working set selection is an important technique, and some exciting
schemes were employed into this field. To improve working set selection, we
propose a new model for working set selection in sequential minimal
optimization (SMO) decomposition methods. In this model, it selects B as
working set without reselection. Some properties are given by simple proof, and
experiments demonstrate that the proposed method is in general faster than
existing methods.
| A Novel Model of Working Set Selection for SMO Decomposition Methods In the process of training Support Vector Machines (SVMs) by decomposition
methods, working set selection is an important technique, and some exciting
schemes were employed into this field. To improve working set selection, we
propose a new model for working set selection in sequential minimal
optimization (SMO) decomposition methods. In this model, it selects B as
working set without reselection. Some properties are given by simple proof, and
experiments demonstrate that the proposed method is in general faster than
existing methods.
| [
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] |
16 | 16 | Getting started in probabilistic graphical models | Probabilistic graphical models (PGMs) have become a popular tool for
computational analysis of biological data in a variety of domains. But, what
exactly are they and how do they work? How can we use PGMs to discover patterns
that are biologically relevant? And to what extent can PGMs help us formulate
new hypotheses that are testable at the bench? This note sketches out some
answers and illustrates the main ideas behind the statistical approach to
biological pattern discovery.
| Getting started in probabilistic graphical models Probabilistic graphical models (PGMs) have become a popular tool for
computational analysis of biological data in a variety of domains. But, what
exactly are they and how do they work? How can we use PGMs to discover patterns
that are biologically relevant? And to what extent can PGMs help us formulate
new hypotheses that are testable at the bench? This note sketches out some
answers and illustrates the main ideas behind the statistical approach to
biological pattern discovery.
| [
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] |
17 | 17 | A tutorial on conformal prediction | Conformal prediction uses past experience to determine precise levels of
confidence in new predictions. Given an error probability $\epsilon$, together
with a method that makes a prediction $\hat{y}$ of a label $y$, it produces a
set of labels, typically containing $\hat{y}$, that also contains $y$ with
probability $1-\epsilon$. Conformal prediction can be applied to any method for
producing $\hat{y}$: a nearest-neighbor method, a support-vector machine, ridge
regression, etc.
Conformal prediction is designed for an on-line setting in which labels are
predicted successively, each one being revealed before the next is predicted.
The most novel and valuable feature of conformal prediction is that if the
successive examples are sampled independently from the same distribution, then
the successive predictions will be right $1-\epsilon$ of the time, even though
they are based on an accumulating dataset rather than on independent datasets.
In addition to the model under which successive examples are sampled
independently, other on-line compression models can also use conformal
prediction. The widely used Gaussian linear model is one of these.
This tutorial presents a self-contained account of the theory of conformal
prediction and works through several numerical examples. A more comprehensive
treatment of the topic is provided in "Algorithmic Learning in a Random World",
by Vladimir Vovk, Alex Gammerman, and Glenn Shafer (Springer, 2005).
| A tutorial on conformal prediction Conformal prediction uses past experience to determine precise levels of
confidence in new predictions. Given an error probability $\epsilon$, together
with a method that makes a prediction $\hat{y}$ of a label $y$, it produces a
set of labels, typically containing $\hat{y}$, that also contains $y$ with
probability $1-\epsilon$. Conformal prediction can be applied to any method for
producing $\hat{y}$: a nearest-neighbor method, a support-vector machine, ridge
regression, etc.
Conformal prediction is designed for an on-line setting in which labels are
predicted successively, each one being revealed before the next is predicted.
The most novel and valuable feature of conformal prediction is that if the
successive examples are sampled independently from the same distribution, then
the successive predictions will be right $1-\epsilon$ of the time, even though
they are based on an accumulating dataset rather than on independent datasets.
In addition to the model under which successive examples are sampled
independently, other on-line compression models can also use conformal
prediction. The widely used Gaussian linear model is one of these.
This tutorial presents a self-contained account of the theory of conformal
prediction and works through several numerical examples. A more comprehensive
treatment of the topic is provided in "Algorithmic Learning in a Random World",
by Vladimir Vovk, Alex Gammerman, and Glenn Shafer (Springer, 2005).
| [
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] |
18 | 18 | Scale-sensitive Psi-dimensions: the Capacity Measures for Classifiers
Taking Values in R^Q | Bounds on the risk play a crucial role in statistical learning theory. They
usually involve as capacity measure of the model studied the VC dimension or
one of its extensions. In classification, such "VC dimensions" exist for models
taking values in {0, 1}, {1,..., Q} and R. We introduce the generalizations
appropriate for the missing case, the one of models with values in R^Q. This
provides us with a new guaranteed risk for M-SVMs which appears superior to the
existing one.
| Scale-sensitive Psi-dimensions: the Capacity Measures for Classifiers
Taking Values in R^Q Bounds on the risk play a crucial role in statistical learning theory. They
usually involve as capacity measure of the model studied the VC dimension or
one of its extensions. In classification, such "VC dimensions" exist for models
taking values in {0, 1}, {1,..., Q} and R. We introduce the generalizations
appropriate for the missing case, the one of models with values in R^Q. This
provides us with a new guaranteed risk for M-SVMs which appears superior to the
existing one.
| [
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