Selecting the optimal kernel is an important and difficult challenge in applying kernel methods to pattern recognition. To address this challenge, multiple kernel learning (MKL) aims to learn a kernel from a combination of base kernel functions that perform optimally on the task. In this paper, we propose a novel MKL-themed approach to combine base kernels that are multiplicatively shaped with low-rank positive semidefinitve matrices. The proposed approach generalizes several popular MKL methods and thus provides more flexibility in modeling data. Computationally, we show how these low-rank matrices can be learned efficiently from data using convex quadratic programming. Empirical studies on several standard benchmark datasets for MKL show that the new approach often improves prediction accuracy statistically significantly over very competitive single kernel and other MKL methods.

In many real applications, especially those involving data objects with complicated semantics, it is generally desirable to discover the relation between patterns in the input space and labels corresponding to different semantics in the output space. This task becomes feasible with MIML (Multi-Instance Multi-Label learning), a recently developed learning framework, where each data object is represented by multiple instances and is allowed to be associated with multiple labels simultaneously. In this paper, we propose KISAR , an MIML algorithm that is able to discover what instances trigger what labels. By considering the fact that highly relevant labels usually share some patterns, we develop a convex optimization formulation and provide an alternating optimization solution. Experiments show that KISAR is able to discover reasonable relations between input patterns and output labels, and achieves performances that are highly competitive with many state-of-the-art MIML algorithms.

A “hub” is an object closely surrounded by, or very similar to, many other objects in the dataset. Recent studies by Radovanovi´c et al. indicate that in high dimensional spaces, hubs almost always emerge, and objects close to the data centroid tend to become hubs. In this paper, we show that the family of kernels based on the graph Laplacian makes all objects in the dataset equally similar to the centroid, and thus they are expected to make less hubs when used as a similarity measure. We investigate this hypothesis using both synthetic and real-world data. It turns out that these kernels suppress hubs in some cases but not always, and the results seem to be affected by the size of the data—a factor not discussed previously. However, for the datasets in which hubs are indeed reduced by the Laplacian-based kernels, these kernels work well in ranking and classification tasks. This result suggests that the amount of hubs, which can be readily computed in an unsupervised fashion, can be a yardstick of whether Laplacian-based kernels work effectively for a given data.

Predicting entailment between two given texts is an important task upon which the performance of numerous NLP tasks depend on such as question answering, text summarization, and information extraction. The degree to which two texts are similar has been used extensively as a key feature in much previous work in predicting entailment. However, using similarity scores directly, without proper transformations, results in suboptimal performance. Given a set of lexical similarity measures, we propose a method that jointly learns both (a) a set of non-linear transformation functions for those similarity measures and, (b) the optimal non-linear combination of those transformation functions to predict textual entailment. Our method consistently outperforms numerous baselines, reporting a micro-averaged F-score of 46.48 on the RTE- 7 benchmark dataset. The proposed method is ranked 2-nd among 33 entailment systems participated in RTE-7, demonstrating its competitiveness over numerous other entailment approaches. Although our method is statistically comparable to the current state-of-the-art, we require less external knowledge resources.

In this paper, we address the problem of continually parsing a stream of 3D point cloud data acquired from a laser sensor mounted on a road vehicle. We leverage an online star clustering algorithm coupled with an incremental belief update in an evolving undirected graphical model. The fusion of these techniques allows the robot to parse streamed data and to continually improve its understanding of the world. The core competency produced is an ability to infer object classes from similarities based on appearance and shape features, and to concurrently combine that with a spatial smoothing algorithm incorporating geometric consistency. This formulation of feature-space star clustering modulating the potentials of a spatial graphical model is entirely novel. In our method, the two sources of information: feature similarity and geometrical consistency are fed continu- ally into the system, improving the belief over the class distributions as new data arrives. The algorithm obviates the need for hand-labeled training data and makes no apriori assumptions on the number or characteristics of object categories. Rather, they are learnt incrementally over time from streamed input data. In experiments per- formed on real 3D laser data from an outdoor scene, we show that our approach is capable of obtaining an ever- improving unsupervised scene categorization.

Event extraction systems typically locate the role fillers for an event by analyzing sentences in isolation and identifying each role filler independently of the others. We argue that more accurate event extraction requires a view of the larger context to decide whether an entity is related to a relevant event. We propose a bottom-up approach to event extraction that initially identifies candidate role fillers independently and then uses that information as well as discourse properties to model textual cohesion. The novel component of the architecture is a sequentially structured sentence classifier that identifies event-related story contexts. The sentence classifier uses lexical associations and discourse relations across sentences, as well as domain-specific distributions of candidate role fillers within and across sentences. This approach yields state-of-the-art performance on the MUC-4 data set, achieving substantially higher precision than previous systems.

Exemplar-based clustering methods have been extensively shown to be effective in many clustering problems. They adaptively determine the number of clusters and hold the appealing advantage of not requiring the estimation of latent parameters, which is otherwise difficult in case of complicated parametric model and high dimensionality of the data. However, modeling arbitrary underlying distribution of the data is still difficult for existing exemplar-based clustering methods. We present Pairwise Exemplar Clustering (PEC) to alleviate this problem by modeling the underlying cluster distributions more accurately with non-parametric kernel density estimation. Interpreting the clusters as classes from a supervised learning perspective, we search for an optimal partition of the data that balances two quantities: 1 the misclassification rate of the data partition for separating the clusters; 2 the sum of within-cluster dissimilarities for controlling the cluster size. The broadly used kernel form of cut turns out to be a special case of our formulation. Moreover, we optimize the corresponding objective function by a new efficient algorithm for message computation in a pairwise MRF. Experimental results on synthetic and real data demonstrate the effectiveness of our method.

This study considers the problem of feature selection in incomplete data. The intuitive approach is to first impute the missing values, and then apply a standard feature selection method to select relevant features. In this study, we show how to perform feature selection directly, without imputing missing values. We define the objective function of the uncertainty margin-based feature selection method to maximize each instance’s uncertainty margin in its own relevant subspace. In optimization, we take into account the uncertainty of each instance due to the missing values. The experimental results on synthetic and 6 benchmark data sets with few missing values (less than 25%) provide evidence that our method can select the same accurate features as the alternative methods which apply an imputation method first. However, when there is a large fraction of missing values (more than 25%) in data, our feature selection method outperforms the alternatives, which impute missing values first.

Causal inference uses observations to infer the causal structure of the data generating system. We study a class of functional models that we call Time Series Models with Independent Noise (TiMINo). These models require independent residual time series, whereas traditional methods like Granger causality exploit the variance of residuals. There are two main contributions: (1) Theoretical: By restricting the model class (e.g. to additive noise) we can provide a more general identifiability result than existing ones. This result incorporates lagged and instantaneous effects that can be nonlinear and do not need to be faithful, and non-instantaneous feedbacks between the time series. (2) Practical: If there are no feedback loops between time series, we propose an algorithm based on non-linear independence tests of time series. When the data are causally insufficient, or the data generating process does not satisfy the model assumptions, this algorithm may still give partial results, but mostly avoids incorrect answers. An extension to (non-instantaneous) feedbacks is possible, but not discussed. It outperforms existing methods on artificial and real data. Code can be provided upon request.

The problem of hierarchical clustering items from pairwise similarities is found across various scientific disciplines, from biology to networking. Often, applications of clustering techniques are limited by the cost of obtaining similarities between pairs of items. While prior work has been developed to reconstruct clustering using a significantly reduced set of pairwise similarities via adaptive measurements, these techniques are only applicable when choice of similarities are available to the user. In this paper, we examine reconstructing hierarchical clustering under similarity observations at-random. We derive precise bounds which show that a significant fraction of the hierarchical clustering can be recovered using fewer than all the pairwise similarities. We find that the correct hierarchical clustering down to a constant fraction of the total number of items (i.e., clusters sized O(N)) can be found using only O(N log N) randomly selected pairwise similarities in expectation.