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571
Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers
, 2010
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Markov Logic Networks
 MACHINE LEARNING
, 2006
"... We propose a simple approach to combining firstorder logic and probabilistic graphical models in a single representation. A Markov logic network (MLN) is a firstorder knowledge base with a weight attached to each formula (or clause). Together with a set of constants representing objects in the ..."
Abstract

Cited by 816 (39 self)
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We propose a simple approach to combining firstorder logic and probabilistic graphical models in a single representation. A Markov logic network (MLN) is a firstorder knowledge base with a weight attached to each formula (or clause). Together with a set of constants representing objects in the domain, it specifies a ground Markov network containing one feature for each possible grounding of a firstorder formula in the KB, with the corresponding weight. Inference in MLNs is performed by MCMC over the minimal subset of the ground network required for answering the query. Weights are efficiently learned from relational databases by iteratively optimizing a pseudolikelihood measure. Optionally, additional clauses are learned using inductive logic programming techniques. Experiments with a realworld database and knowledge base in a university domain illustrate the promise of this approach.
SNOPT: An SQP Algorithm For LargeScale Constrained Optimization
, 2002
"... Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first deriv ..."
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Cited by 597 (24 self)
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Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first derivatives are available, and that the constraint gradients are sparse. We discuss
Scalable training of L1regularized loglinear models
 In ICML ’07
, 2007
"... The lbfgs limitedmemory quasiNewton method is the algorithm of choice for optimizing the parameters of largescale loglinear models with L2 regularization, but it cannot be used for an L1regularized loss due to its nondifferentiability whenever some parameter is zero. Efficient algorithms have ..."
Abstract

Cited by 178 (5 self)
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The lbfgs limitedmemory quasiNewton method is the algorithm of choice for optimizing the parameters of largescale loglinear models with L2 regularization, but it cannot be used for an L1regularized loss due to its nondifferentiability whenever some parameter is zero. Efficient algorithms have been proposed for this task, but they are impractical when the number of parameters is very large. We present an algorithm OrthantWise Limitedmemory QuasiNewton (owlqn), based on lbfgs, that can efficiently optimize the L1regularized loglikelihood of loglinear models with millions of parameters. In our experiments on a parse reranking task, our algorithm was several orders of magnitude faster than an alternative algorithm, and substantially faster than lbfgs on the analogous L2regularized problem. We also present a proof that owlqn is guaranteed to converge to a globally optimal parameter vector. 1.
Representations Of QuasiNewton Matrices And Their Use In Limited Memory Methods
, 1996
"... We derive compact representations of BFGS and symmetric rankone matrices for optimization. These representations allow us to efficiently implement limited memory methods for large constrained optimization problems. In particular, we discuss how to compute projections of limited memory matrices onto ..."
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Cited by 160 (11 self)
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We derive compact representations of BFGS and symmetric rankone matrices for optimization. These representations allow us to efficiently implement limited memory methods for large constrained optimization problems. In particular, we discuss how to compute projections of limited memory matrices onto subspaces. We also present a compact representation of the matrices generated by Broyden's update for solving systems of nonlinear equations.
Gaussian processes for ordinal regression
 Journal of Machine Learning Research
, 2004
"... We present a probabilistic kernel approach to ordinal regression based on Gaussian processes. A threshold model that generalizes the probit function is used as the likelihood function for ordinal variables. Two inference techniques, based on the Laplace approximation and the expectation propagation ..."
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Cited by 116 (4 self)
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We present a probabilistic kernel approach to ordinal regression based on Gaussian processes. A threshold model that generalizes the probit function is used as the likelihood function for ordinal variables. Two inference techniques, based on the Laplace approximation and the expectation propagation algorithm respectively, are derived for hyperparameter learning and model selection. We compare these two Gaussian process approaches with a previous ordinal regression method based on support vector machines on some benchmark and realworld data sets, including applications of ordinal regression to collaborative filtering and gene expression analysis. Experimental results on these data sets verify the usefulness of our approach.
Exponentiated gradient algorithms for conditional random fields and maxmargin Markov networks
, 2008
"... Loglinear and maximummargin models are two commonlyused methods in supervised machine learning, and are frequently used in structured prediction problems. Efficient learning of parameters in these models is therefore an important problem, and becomes a key factor when learning from very large dat ..."
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Cited by 94 (2 self)
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Loglinear and maximummargin models are two commonlyused methods in supervised machine learning, and are frequently used in structured prediction problems. Efficient learning of parameters in these models is therefore an important problem, and becomes a key factor when learning from very large data sets. This paper describes exponentiated gradient (EG) algorithms for training such models, where EG updates are applied to the convex dual of either the loglinear or maxmargin objective function; the dual in both the loglinear and maxmargin cases corresponds to minimizing a convex function with simplex constraints. We study both batch and online variants of the algorithm, and provide rates of convergence for both cases. In the maxmargin case, O ( 1 ε) EG updates are required to reach a given accuracy ε in the dual; in contrast, for loglinear models only O(log (1/ε)) updates are required. For both the maxmargin and loglinear cases, our bounds suggest that the online EG algorithm requires a factor of n less computation to reach a desired accuracy than the batch EG algorithm, where n is the number of training examples. Our experiments confirm that the online algorithms are much faster than the batch algorithms in practice. We describe how the EG updates factor in a convenient way for structured prediction problems, allowing the algorithms to be
A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability
, 2005
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A scalable modular convex solver for regularized risk minimization
 In KDD. ACM
, 2007
"... A wide variety of machine learning problems can be described as minimizing a regularized risk functional, with different algorithms using different notions of risk and different regularizers. Examples include linear Support Vector Machines (SVMs), Logistic Regression, Conditional Random Fields (CRFs ..."
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Cited by 78 (16 self)
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A wide variety of machine learning problems can be described as minimizing a regularized risk functional, with different algorithms using different notions of risk and different regularizers. Examples include linear Support Vector Machines (SVMs), Logistic Regression, Conditional Random Fields (CRFs), and Lasso amongst others. This paper describes the theory and implementation of a highly scalable and modular convex solver which solves all these estimation problems. It can be parallelized on a cluster of workstations, allows for datalocality, and can deal with regularizers such as ℓ1 and ℓ2 penalties. At present, our solver implements 20 different estimation problems, can be easily extended, scales to millions of observations, and is up to 10 times faster than specialized solvers for many applications. The open source code is freely available as part of the ELEFANT toolbox.