We consider a general form of transductive learning on graphs with Laplacian regularization, and derive margin-based generalization bounds using appropriate geometric properties of the graph. We use this analysis to obtain a better understanding of the role of normalization of the graph Laplacian matrix as well as the effect of dimension reduction. The results suggest a limitation of the standard degree-based normalization. We propose a remedy from our analysis and demonstrate empirically that the remedy leads to improved classification performance.

We describe an unsupervised method for learning a probabilistic grammar of an object from a set of training examples. Our approach is invariant to the scale and rotation of the objects. We illustrate our approach using thirteen objects from the Caltech 101 database. In addition, we learn the model of a hybrid object class where we do not know the specific object or its position, scale or pose. This is illustrated by learning a hybrid class consisting of faces, motorbikes, and airplanes. The individual objects can be recovered as different aspects of the grammar for the object class.

In this paper, we formalize multi-instance multi-label learning, where each training example is associated with not only multiple instances but also multiple class labels. Such a problem can occur in many real-world tasks, e.g. an image usually contains multiple patches each of which can be described by a feature vector, and the image can belong to multiple categories since its semantics can be recognized in different ways. We analyze the relationship between multi-instance multi-label learning and the learning frameworks of traditional supervised learning, multiinstance learning and multi-label learning.

Semi-supervised learning algorithms have been successfully applied in many applications with scarce labeled data, by utilizing the unlabeled data. One important category is graph based semi-supervised learning algorithms, for which the performance depends considerably on the quality of the graph, or its hyperparameters. In this paper, we deal with the less explored problem of learning the graphs. We propose a graph learning method for the harmonic energy minimization method; this is done by minimizing the leave-one-out prediction error on labeled data points. We use a gradient based method and designed an efficient algorithm which significantly accelerates the calculation of the gradient by applying the matrix inversion lemma and using careful pre-computation. Experimental results show that the graph learning method is effective in improving the performance of the classification algorithm.

We consider the problem of grasping novel objects, specifically ones that are being seen for the first time through vision. We present a learning algorithm that neither requires, nor tries to build, a 3d model of the object. Instead it predicts, directly as a function of the images, a point at which to grasp the object. Our algorithm is trained via supervised learning, using synthetic images for the training set. We demonstrate on a robotic manipulation platform that this approach successfully grasps a wide variety of objects, such as wine glasses, duct tape, markers, a translucent box, jugs, knife-cutters, cellphones, keys, screwdrivers, staplers, toothbrushes, a thick coil of wire, a strangely shaped power horn, and others, none of which were seen in the training set.

The Maximum Margin Planning (MMP) (Ratliff et al., 2006) algorithm solves imitation learning problems by learning linear mappings from features to cost functions in a planning domain. The learned policy is the result of minimum-cost planning using these cost functions. These mappings are chosen so that example policies (or trajectories) given by a teacher appear to be lower cost (with a lossscaled margin) than any other policy for a given planning domain.

Kernel-based regularized learning seeks a model in a hypothesis space by minimizing the empirical error and the model's complexity. Based on the representer theorem, the solution consists of a linear combination of translates of a kernel. This paper investigates a generalized form of representer theorem for kernel-based learning. After mapping predefined features and translates of a kernel simultaneously onto a hypothesis space by a specific way of constructing kernels, we proposed a new algorithm by utilizing a generalized regularizer which leaves part of the space unregularized. Using a squared-loss function in calculating the empirical error, a simple convex solution is obtained which combines predefined features with translates of the kernel. Empirical evaluations have confirmed the effectiveness of the algorithm for supervised learning tasks.

Everyday inductive reasoning draws on many kinds of knowledge, including knowledge about relationships between properties and knowledge about relationships between objects. Previous accounts of inductive reasoning generally focus on just one kind of knowledge: models of causal reasoning often focus on relationships between properties, and models of similarity-based reasoning often focus on similarity relationships between objects. We present a Bayesian model of inductive reasoning that incorporates both kinds of knowledge, and show that it accounts well for human inferences about the properties of biological species.

This work presents a method for estimating human facial attractiveness, based on supervised learning techniques. Numerous facial features that describe facial geometry, color and texture, combined with an average human attractiveness score for each facial image, are used to train various predictors. Facial attractiveness ratings produced by the final predictor are found to be highly correlated with human ratings, markedly improving previous machine learning achievements. Simulated psychophysical experiments with virtually manipulated images reveal preferences in the machine's judgments which are remarkably similar to those of humans. These experiments shed new light on existing theories of facial attractiveness such as the averageness, smoothness and symmetry hypotheses. It is intriguing to find that a machine trained explicitly to capture an operational performance criteria such as attractiveness rating, implicitly captures basic human psychophysical biases characterizing the perception of facial attractiveness in general.

We consider a general form of transductive learning on graphs with Laplacian regularization, and derive margin-based generalization bounds using appropriate geometric properties of the graph. We use this analysis to obtain a better understanding of the role of normalization of the graph Laplacian matrix as well as the effect of dimension reduction. The results suggest a limitation of the standard degree-based normalization. We propose a remedy from our analysis and demonstrate empirically that the remedy leads to improved classification performance.