In this paper, we provide a general theorem that establishes a correspondence betweensurrogate loss functions in classification and the family of f-divergences. Moreover, we provide constructive procedures for determining the f-divergence induced by a given surrogate loss, and conversely for finding all surrogate loss functions that realize a given f-divergence. Next we introduce the notion of universal equivalence among loss functions and corresponding f-divergences, and provide necessary andsufficient conditions for universal equivalence to hold. These ideas have applications to classification problems that also involve a component ofexperiment design; in particular, we leverage our results to prove consistency of a procedure for learning a classifier under decentralization requirements.

We present a novel spectral clustering method that enables users to incorporate priorknowledge of the size of clusters into the clustering process. The cost function, which is named size regularized cut (SRcut), is defined as the sum of the inter-cluster similarity and a regularization term measuring therelative size of two clusters. Finding a partition of the data set to minimize SRcut is proved to be NPcomplete. An approximation algorithm isproposed to solve a relaxed version of the optimization problem as an eigenvalue problem. Evaluations over different data sets demonstrate thatthe method is not sensitive to outliers and performs better than normalized cut.

Suppose we have a set of training data (ztcl7 yl), . . .

Linear text classification algorithms work by computing an inner product betweena test document vector and a parameter vector. In many such algorithms, including naive Bayes and most TFIDF variants, the parameters aredetermined by some simple, closed-form, function of training set statistics; we call this mapping mapping from statistics to parameters, the parameter function. Much research in text classification over the last few decades has consisted of manual efforts to identify better parameter functions. Inthis paper, we propose an algorithm for automatically learning this function from related classification problems. The parameter function foundby our algorithm then defines a new learning algorithm for text classification, which we can apply to novel classification tasks. We find that our learned classifier outperforms existing methods on a variety of multiclass text classification tasks.

We show that Queyranne's algorithm for minimizing symmetric submodular functionscan be used for clustering with a variety of different objective functions. Two specific criteria that we consider in this paper are the single linkage and the minimum description length criteria. The first criterion triesto maximize the minimum distance between elements of different clusters,and is inherently "discriminative". It is known that optimal clusterings into k clusters for any given k in polynomial time for this criterion can be computed. The second criterion seeks to minimize the description length of the clusters given a probabilistic generative model. We show that the optimal partitioning into 2 clusters, and approximate partitioning (guaranteed to be within a factor of 2 of the the optimal) for more clusters can be computed. To the best of our knowledge, this is the first time that a tractable algorithm for finding the optimal clustering with respect to the MDL criterion for 2 clusters has been given. Besides the optimality result for the MDL criterion, the chief contribution of this paper is to show that the same algorithm can be used to optimize a broad class of criteria, and hence can be used for many application specific criterion for which efficient algorithm are not known.

Fusing multiple information sources can yield significant benefits to successfully accomplishlearning tasks. Many studies have focussed on fusing information in supervised learning contexts. We present an approach to utilize multiple information sources in the form of similarity data for unsupervised learning. Based on similarity information, the clustering task is phrased as a nonnegative matrix factorization problem of a mixture ofsimilarity measurements. The tradeoff between the informativeness ofdata sources and the sparseness of their mixture is controlled by an entropy-based weighting mechanism. For the purpose of model selection, astability-based approach is employed to ensure the selection of the most self-consistent hypothesis. The experiments demonstrate the performance of the method on toy as well as real world data sets.

This activity often manifests itself as dynamically coordinated sequences of action potentials. Since multiple electrode recordings are now a standard tool in neuroscience research, it is important to have a measure of such network-wide behavioral coordinationand information sharing, applicable to multiple neural spike train data. We propose a new statistic, informational coherence, which measures how much better one unit can be predicted by knowing the dynamical state of another. We argue informational coherence is a measure of association and shared information which is superior to traditional pairwisemeasures of synchronization and correlation. To find the dynamical states, we use a recently-introduced algorithm which reconstructs effectivestate spaces from stochastic time series.

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.

Online learning algorithms are typically fast, memory efficient, and simple toimplement. However, many common learning problems fit more naturally in the batch learning setting. The power of online learning algorithms can be exploited in batch settings by using online-to-batch conversions techniques which build a new batch algorithm from an existing onlinealgorithm. We first give a unified overview of three existing online-to-batch conversion techniques which do not use training data in the conversion process. We then build upon these data-independent conversions to derive and analyze data-driven conversions.

We propose a probabilistic model based on Independent Component Analysis for learning multiple related tasks. In our model the task parameters areassumed to be generated from independent sources which account for the relatedness of the tasks. We use Laplace distributions to model hidden sources which makes it possible to identify the hidden, independent components instead of just modeling correlations. Furthermore, ourmodel enjoys a sparsity property which makes it both parsimonious and robust. We also propose efficient algorithms for both empirical Bayes method and point estimation. Our experimental results on two multi-label text classification data sets show that the proposed approach is promising.