It is well-known that everything that is learnable in the difficult online setting, where an arbitrary sequences of examples must be labeled one at a time, is also learnable in the batch setting, where examples are drawn independently from a distribution. We show a result in the opposite direction. We give an efficient conversion algorithm from batch to online that is transductive: it uses future unlabeled data. This demonstrates the equivalence between what is properly and efficiently learnable in a batch model and a transductive online model.

There is little consensus about the computational function of top-down synaptic connections in the visual system. Here we explore the hypothesis that top-down connections, like bottom-up connections, reflect partwhole relationships. We analyze a recurrent network with bidirectional synaptic interactions between a layer of neurons representing parts and a layer of neurons representing wholes. Within each layer, there is lateral inhibition. When the network detects a whole, it can rigorously enforce part-whole relationships by ignoring parts that do not belong.

This paper presents representation and logic for labeling contrast edges and ridges in visual scenes in terms of both surface occlusion (border ownership) and thinline objects. In natural scenes, thinline objects include sticks and wires, while in human graphical communication thinlines include connectors, dividers, and other abstract devices. Our analysis is directed at both natural and graphical domains. The basic problem is to formulate the logic of the interactions among local image events, specifically contrast edges, ridges, junctions, and alignment relations, such as to encode the natural constraints among these events in visual scenes. In a sparse heterogeneous Markov Random Field framework, we define a set of interpretation nodes and energy/potential functions among them. The minimum energy configuration found by Loopy Belief Propagation is shown to correspond to preferred human interpretation across a wide range of prototypical examples including important illusory contour figures such as the Kanizsa Triangle, as well as more difficult examples. In practical terms, the approach delivers correct interpretations of inherently ambiguous hand-drawn box-and-connector diagrams at low computational cost.

We introduce a technique for dimensionality estimation based on the notion of quantization dimension, which connects the asymptotic optimal quantization error for a probability distribution on a manifold to its intrinsic dimension. The definition of quantization dimension yields a family of estimation algorithms, whose limiting case is equivalent to a recent method based on packing numbers. Using the formalism of high-rate vector quantization, we address issues of statistical consistency and analyze the behavior of our scheme in the presence of noise.

To investigate how top-down (TD) and bottom-up (BU) information is weighted in the guidance of human search behavior, we manipulated the proportions of BU and TD components in a saliency-based model. The model is biologically plausible and implements an artificial retina and a neuronal population code. The BU component is based on featurecontrast. The TD component is defined by a feature-template match to a stored target representation. We compared the model's behavior at different mixtures of TD and BU components to the eye movement behavior of human observers performing the identical search task. We found that a purely TD model provides a much closer match to human behavior than any mixture model using BU information. Only when biological constraints are removed (e.g., eliminating the retina) did a BU/TD mixture model begin to approximate human behavior.

Sets", we consider the problem of retrieving items from a concept or cluster, given a query consisting of a few items from that cluster. We formulate this as a Bayesian inference problem and describe a very simple algorithm for solving it. Our algorithm uses a modelbased concept of a cluster and ranks items using a score which evaluates the marginal probability that each item belongs to a cluster containing the query items. For exponential family models with conjugate priors this marginal probability is a simple function of sufficient statistics. We focus on sparse binary data and show that our score can be evaluated exactly using a single sparse matrix multiplication, making it possible to apply our algorithm to very large datasets. We evaluate our algorithm on three datasets: retrieving movies from EachMovie, finding completions of author sets from the NIPS dataset, and finding completions of sets of words appearing in the Grolier encyclopedia.

There is experimental evidence that cortical neurons show avalanche activity with the intensity of firing events being distributed as a power-law. We present a biologically plausible extension of a neural network which exhibits a power-law avalanche distribution for a wide range of connectivity parameters.

We present a novel spectral clustering method that enables users to incorporate prior knowledge 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 the relative size of two clusters. Finding a partition of the data set to minimize SRcut is proved to be NPcomplete. An approximation algorithm is proposed to solve a relaxed version of the optimization problem as an eigenvalue problem. Evaluations over different data sets demonstrate that the method is not sensitive to outliers and performs better than normalized cut.

Many real-world classification problems involve the prediction of multiple interdependent variables forming some structural dependency. Recent progress in machine learning has mainly focused on supervised classification of such structured variables. In this paper, we investigate structured classification in a semi-supervised setting. We present a discriminative approach that utilizes the intrinsic geometry of input patterns revealed by unlabeled data points and we derive a maximum-margin formulation of semi-supervised learning for structured variables. Unlike transductive algorithms, our formulation naturally extends to new test points.

Linear text classification algorithms work by computing an inner product between a test document vector and a parameter vector. In many such algorithms, including naive Bayes and most TFIDF variants, the parameters are determined 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. In this paper, we propose an algorithm for automatically learning this function from related classification problems. The parameter function found by 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.