Convexity has recently received a lot of attention in the machine learning community, and the lack of convexity has been seen as a major disadvantage ofmany learning algorithms, such as multi-layer artificial neural networks. We show that training multi-layer neural networks in which the number of hidden units is learned can be viewed as a convex optimization problem. This problem involves an infinite number of variables, but can be solved by incrementally inserting a hidden unit at a time, each time finding a linear classifier that minimizes a weighted sum of errors.

Our understanding of the input-output function of single cells has been substantially advanced by biophysically accurate multi-compartmental models. The large number of parameters needing hand tuning in these models has, however, somewhat hampered their applicability and interpretability. Herewe propose a simple and well-founded method for automatic estimation of many of these key parameters: 1) the spatial distribution of channel densities on the cell's membrane; 2) the spatiotemporal pattern of synaptic input; 3) the channels' reversal potentials; 4) the intercompartmental conductances;and 5) the noise level in each compartment. We assume experimental access to: a) the spatiotemporal voltage signal in the dendrite (or some contiguous subpart thereof, e.g.

Semantic taxonomies such as WordNet provide a rich source of knowledge for natural language processing applications, but are expensive to build, maintain, and extend. Motivated by the problem of automatically constructing and extending such taxonomies, in this paper we present a new algorithm for automatically learning hypernym (isa) relations from text. Our method generalizes earlier work that had relied on using small numbers of handcrafted regular expression patterns to identify hypernym pairs. Using "dependency path" features extracted from parse trees, we introduce a general-purpose formalization and generalization of these patterns. Given a training set of text containing known hypernym pairs, our algorithm automatically extracts useful dependency paths and applies them to new corpora to identify novel pairs. On our evaluation task (determining whether two nouns in a news article participate in a hypernym relationship), our automatically extracted database of hypernyms attains both higher precision and higher recall than WordNet.

We devise and experiment with a dynamical kernel-based system for tracking hand movements from neural activity. The state of the system corresponds to the hand location, velocity, and acceleration, while the system's input are the instantaneous spike rates. The system's state dynamics is defined as a combination of a linear mapping from the previous estimated state and a kernel-based mapping tailored for modeling neural activities. In contrast to generative models, the activity-to-state mapping is learned using discriminative methods by minimizing a noise-robust loss function. We use this approach to predict hand trajectories on the basis of neural activity in motor cortex of behaving monkeys and find that the proposed approach is more accurate than both a static approach based on support vector regression and the Kalman filter.

We present a competitive analysis of Bayesian learning algorithms in the online learning setting and show that many simple Bayesian algorithms (such as Gaussian linear regression and Bayesian logistic regression) perform favorably when compared, in retrospect, to the single best model in the model class. The analysis does not assume that the Bayesian algorithms' modeling assumptions are "correct," and our bounds hold even if the data is adversarially chosen. For Gaussian linear regression (using logloss), our error bounds are comparable to the best bounds in the online learning literature, and we also provide a lower bound showing that Gaussian linear regression is optimal in a certain worst case sense. We also give bounds for some widely used maximum a posteriori (MAP) estimation algorithms, including regularized logistic regression.

The problem of learning a sparse conic combination of kernel functions or kernel matrices for classification or regression can be achieved via the regularization by a block 1-norm [1]. In this paper, we present an algorithm that computes the entire regularization path for these problems. The path is obtained by using numerical continuation techniques, and involves a running time complexity that is a constant times the complexity of solving the problem for one value of the regularization parameter. Working in the setting of kernel linear regression and kernel logistic regression, we show empirically that the effect of the block 1-norm regularization differs notably from the (non-block) 1-norm regularization commonly used for variable selection, and that the regularization path is of particular value in the block case.

Semantic taxonomies such as WordNet provide a rich source of knowledge for natural language processing applications, but are expensive to build, maintain, and extend. Motivated by the problem of automatically constructing and extending such taxonomies, in this paper we present a new algorithm for automatically learning hypernym (isa) relations from text. Our method generalizes earlier work that had relied on using small numbers of handcrafted regular expression patterns to identify hypernym pairs. Using "dependency path" features extracted from parse trees, we introduce a general-purpose formalization and generalization of these patterns. Given a training set of text containing known hypernym pairs, our algorithm automatically extracts useful dependency paths and applies them to new corpora to identify novel pairs. On our evaluation task (determining whether two nouns in a news article participate in a hypernym relationship), our automatically extracted database of hypernyms attains both higher precision and higher recall than WordNet.

We devise and experiment with a dynamical kernel-based system for tracking hand movements from neural activity. The state of the system corresponds to the hand location, velocity, and acceleration, while the system's input are the instantaneous spike rates. The system's state dynamics is defined as a combination of a linear mapping from the previous estimated state and a kernel-based mapping tailored for modeling neural activities. In contrast to generative models, the activity-to-state mapping is learned using discriminative methods by minimizing a noise-robust loss function. We use this approach to predict hand trajectories on the basis of neural activity in motor cortex of behaving monkeys and find that the proposed approach is more accurate than both a static approach based on support vector regression and the Kalman filter.

We present a competitive analysis of Bayesian learning algorithms in the online learning setting and show that many simple Bayesian algorithms (such as Gaussian linear regression and Bayesian logistic regression) perform favorably when compared, in retrospect, to the single best model in the model class. The analysis does not assume that the Bayesian algorithms' modeling assumptions are "correct," and our bounds hold even if the data is adversarially chosen. For Gaussian linear regression (using logloss), our error bounds are comparable to the best bounds in the online learning literature, and we also provide a lower bound showing that Gaussian linear regression is optimal in a certain worst case sense. We also give bounds for some widely used maximum a posteriori (MAP) estimation algorithms, including regularized logistic regression.

The problem of learning a sparse conic combination of kernel functions or kernel matrices for classification or regression can be achieved via the regularization by a block 1-norm [1]. In this paper, we present an algorithm that computes the entire regularization path for these problems. The path is obtained by using numerical continuation techniques, and involves a running time complexity that is a constant times the complexity of solving the problem for one value of the regularization parameter. Working in the setting of kernel linear regression and kernel logistic regression, we show empirically that the effect of the block 1-norm regularization differs notably from the (non-block) 1-norm regularization commonly used for variable selection, and that the regularization path is of particular value in the block case.