Lasso regression tends to assign zero weights to most irrelevant or redundant features, and hence is a promising technique for feature selection. Its limitation, however, is that it only offers solutions to linear models. Kernel machines with feature scaling techniques have been studied for feature selection with nonlinear models. However, such approaches require to solve hard non-convex optimization problems. This paper proposes a new approach named the Feature Vector Machine (FVM). It reformulates the standard Lasso regression into a form isomorphic to SVM, and this form can be easily extended for feature selection with nonlinear models by introducing kernels defined on feature vectors. FVM generates sparse solutions in the nonlinear feature space and it is much more tractable compared to feature scaling kernel machines. Our experiments with FVM on simulated data show encouraging results in identifying the small number of dominating features that are non-linearly correlated to the response, a task the standard Lasso fails to complete.

Lasso regression tends to assign zero weights to most irrelevant or redundant features, and hence is a promising technique for feature selection. Its limitation, however, is that it only offers solutions to linear models. Kernel machines with feature scaling techniques have been studied for feature selection with nonlinear models. However, such approaches require to solve hard non-convex optimization problems. This paper proposes a new approach named the Feature Vector Machine (FVM). It reformulates the standard Lasso regression into a form isomorphic to SVM, and this form can be easily extended for feature selection with nonlinear models by introducing kernels defined on feature vectors. FVM generates sparse solutions in the nonlinear feature space and it is much more tractable compared to feature scaling kernel machines. Our experiments with FVM on simulated data show encouraging results in identifying the small number of dominating features that are non-linearly correlated to the response, a task the standard Lasso fails to complete.

Inner-product operators, often referred to as kernels in statistical learning, define a mapping from some input space into a feature space. The focus of this paper is the construction of biologically-motivated kernels for cortical activities. The kernels we derive, termed Spikernels, map spike count sequences into an abstract vector space in which we can perform various prediction tasks. We discuss in detail the derivation of Spikernels and describe an efficient algorithm for computing their value on any two sequences of neural population spike counts. We demonstrate the merits of our modeling approach using the Spikernel and various standard kernels for the task of predicting hand movement velocities from cortical recordings. In all of our experiments all the kernels we tested outperform the standard scalar product used in regression with the Spikernel consistently achieving the best performance.

Inner-product operators, often referred to as kernels in statistical learning, define a mapping from some input space into a feature space. The focus of this paper is the construction of biologically-motivated kernels for cortical activities. The kernels we derive, termed Spikernels, map spike count sequences into an abstract vector space in which we can perform various prediction tasks. We discuss in detail the derivation of Spikernels and describe an efficient algorithm for computing their value on any two sequences of neural population spike counts. We demonstrate the merits of our modeling approach using the Spikernel and various standard kernels for the task of predicting hand movement velocities from cortical recordings. In all of our experiments all the kernels we tested outperform the standard scalar product used in regression with the Spikernel consistently achieving the best performance.

Inner-product operators, often referred to as kernels in statistical learning, define amapping from some input space into a feature space. The focus of this paper is the construction of biologically-motivated kernels for cortical activities. Thekernels we derive, termed Spikernels, map spike count sequences into an abstract vector space in which we can perform various prediction tasks. We discuss in detail the derivation of Spikernels and describe an efficient algorithm forcomputing their value on any two sequences of neural population spike counts. We demonstrate the merits of our modeling approach using the Spikernel and various standard kernels for the task of predicting hand movement velocitiesfrom cortical recordings. In all of our experiments all the kernels we tested outperform the standard scalar product used in regression with the Spikernel consistently achieving the best performance.

Modern classification applications necessitate supplementing the few available labeled examples with unlabeled examples to improve classification performance. We present a new tractable algorithm for exploiting unlabeled examples in discriminative classification. This is achieved essentially by expanding the input vectors into longer feature vectors via both labeled and unlabeled examples. The resulting classification method can be interpreted as a discriminative kernel density estimate and is readily trained via the EM algorithm, which in this case is both discriminative and achieves the optimal solution. We provide, in addition, a purely discriminative formulation of the estimation problem by appealing to the maximum entropy framework. We demonstrate that the proposed approach requires very few labeled examples for high classification accuracy.

Modern classification applications necessitate supplementing the few available labeled examples with unlabeled examples to improve classification performance. We present a new tractable algorithm for exploiting unlabeled examples in discriminative classification. This is achieved essentially by expanding the input vectors into longer feature vectors via both labeled and unlabeled examples. The resulting classification method can be interpreted as a discriminative kernel density estimate and is readily trained via the EM algorithm, which in this case is both discriminative and achieves the optimal solution. We provide, in addition, a purely discriminative formulation of the estimation problem by appealing to the maximum entropy framework. We demonstrate that the proposed approach requires very few labeled examples for high classification accuracy.

Modern classification applications necessitate supplementing the few available labeled examples with unlabeled examples to improve classification performance.We present a new tractable algorithm for exploiting unlabeled examples in discriminative classification. This is achieved essentially by expanding the input vectors into longer feature vectors via both labeled and unlabeled examples. The resulting classification method can be interpreted as a discriminative kernel density estimate and is readily trainedvia the EM algorithm, which in this case is both discriminative and achieves the optimal solution. We provide, in addition, a purely discriminative formulationof the estimation problem by appealing to the maximum entropy framework. We demonstrate that the proposed approach requiresvery few labeled examples for high classification accuracy.

A key question in vision is how to represent our knowledge of previously encountered objects to classify new ones. The answer depends on how we determine the similarity of two objects. Similarity tells us how relevant each previously seen object is in determining the category to which a new object belongs.

A key question in vision is how to represent our knowledge of previously encountered objects to classify new ones. The answer depends on how we determine the similarity of two objects. Similarity tells us how relevant each previously seen object is in determining the category to which a new object belongs.