Kernel machines such as kernel SVM and kernel ridge regression usually construct high quality models; however, their use in real-world applications remains limited due to the high prediction cost.

A new Bayesian formulation is developed for nonlinear support vector machines (SVMs), based on a Gaussian process and with the SVM hinge loss expressed as a scaled mixture of normals. We then integrate the Bayesian SVM into a factor model, in which feature learning and nonlinear classifier design are performed jointly; almost all previous work on such discriminative feature learning has assumed a linear classifier. Inference is performed with expectation conditional maximization (ECM) and Markov Chain Monte Carlo (MCMC). An extensive set of experiments demonstrate the utility of using a nonlinear Bayesian SVM within discriminative feature learning and factor modeling, from the standpoints of accuracy and interpretability.

Lazy local learning methods train a classifier "on the fly" at test time, using only a subset of the training instances that are most relevant to the novel test example. The goal is to tailor the classifier to the properties of the data surrounding the test example. Existing methods assume that the instances most useful for building the local model are strictly those closest to the test example. However, this fails to account for the fact that the success of the resulting classifier depends on the full distribution of selected training instances. Rather than simply gathering the test example's nearest neighbors, we propose to predict the subset of training data that is jointly relevant to training its local model. We develop an approach to discover patterns between queries and their "good" neighborhoods using large-scale multilabel classification with compressed sensing. Given a novel test point, we estimate both the composition and size of the training subset likely to yield an accurate local model. We demonstrate the approach on image classification tasks on SUN and aPascal and show its advantages over traditional global and local approaches.

In many classification problems, the input is represented as a set of features, e.g., the bag-of-words (BoW) representation of documents. Support vector machines (SVMs) are widely used tools for such classification problems. The performance of the SVMs is generally determined by whether kernel values between data points can be defined properly. However, SVMs for BoW representations have a major weakness in that the co-occurrence of different but semantically similar words cannot be reflected in the kernel calculation. To overcome the weakness, we propose a kernel-based discriminative classifier for BoW data, which we call the latent support measure machine (latent SMM). With the latent SMM, a latent vector is associated with each vocabulary term, and each document is represented as a distribution of the latent vectors for words appearing in the document. To represent the distributions efficiently, we use the kernel embeddings of distributions that hold high order moment information about distributions. Then the latent SMM finds a separating hyperplane that maximizes the margins between distributions of different classes while estimating latent vectors for words to improve the classification performance. In the experiments, we show that the latent SMM achieves state-of-the-art accuracy for BoW text classification, is robust with respect to its own hyper-parameters, and is useful to visualize words.

We propose a structured prediction algorithm for object localization based on Support Vector Machines (SVMs) using privileged information. Privileged information provides useful high-level knowledge for image understanding and facilitates learning a reliable model even with a small number of training examples. In our setting, we assume that such information is available only at training time since it may be difficult to obtain from visual data accurately without human supervision. Our goal is to improve performance by incorporating privileged information into ordinary learning framework and adjusting model parameters for better generalization. We tackle object localization problem based on a novel structural SVM using privileged information, where an alternating loss-augmented inference procedure is employed to handle the term in the objective function corresponding to privileged information. We apply the proposed algorithm to the Caltech-UCSD Birds 200-2011 dataset, and obtain encouraging results suggesting further investigation into the benefit of privileged information in structured prediction.

In many situations we have some measurement of confidence on "positiveness" for a binary label. The "positiveness" is a continuous value whose range is a bounded interval.

Additional Feedback: * One philosophical question that comes to mind when reading the three observations in the Introduction and while going over the example in Figure 1 is the following: Could it be that the exact reason that the representation methods learn interesting patterns is the fact that they are allowed to twist and curve the space as required, in order to bring nodes that are far apart in terms of graph distance close together in terms of Euclidean distance? It is not obvious to me that constraining the optimization algorithm of this ability can only have positive outcome. There's a parallel to be drawn here with the kernel trick in Support Vector Machines, where we are allowed to embed the data in a higher dimension, where the classes become linearly separable. This way, the sum could be defined over (q', q'') \in \Gamma_{i, j} * The sectional curvature could have been more thoroughly introduced. Unfortunately, for a paper that is heavily based on geometric notions, there's a clear shortage of pictures.

This study investigates the internal representations of verb-particle combinations, called multi-word verbs, within transformer-based large language models (LLMs), specifically examining how these models capture lexical and syntactic properties at different neural network layers. Using the BERT architecture, we analyze the representations of its layers for two different verb-particle constructions: phrasal verbs like 'give up' and prepositional verbs like 'look at'. Our methodology includes training probing classifiers on the internal representations to classify these categories at both word and sentence levels. The results indicate that the model's middle layers achieve the highest classification accuracies. To further analyze the nature of these distinctions, we conduct a data separability test using the Generalized Discrimination Value (GDV). While GDV results show weak linear separability between the two verb types, probing classifiers still achieve high accuracy, suggesting that representations of these linguistic categories may be non-linearly separable. This aligns with previous research indicating that linguistic distinctions in neural networks are not always encoded in a linearly separable manner. These findings computationally support usage-based claims on the representation of verb-particle constructions and highlight the complex interaction between neural network architectures and linguistic structures.

We consider the problem in Electrical Impedance Tomography (EIT) of identifying one or multiple inclusions in a background-conducting body $\Omega\subset\mathbb{R}^2$, from the knowledge of a finite number of electrostatic measurements taken on its boundary $\partial\Omega$ and modelled by the Dirichlet-to-Neumann (D-N) matrix. Once the presence of one inclusion in $\Omega$ is established, our model, combined with the machine learning techniques of Artificial Neural Networks (ANN) and Support Vector Machines (SVM), may be used to determine the size of the inclusion, the presence of multiple inclusions, and also that of anisotropy within the inclusion(s). Utilising both real and simulated datasets within a 16-electrode setup, we achieve a high rate of inclusion detection and show that two measurements are sufficient to achieve a good level of accuracy when predicting the size of an inclusion. This underscores the substantial potential of integrating machine learning approaches with the more classical analysis of EIT and the inverse inclusion problem to extract critical insights, such as the presence of anisotropy.

Motion planning is a central challenge in robotics, with learning-based approaches gaining significant attention in recent years. Our work focuses on a specific aspect of these approaches: using machine-learning techniques, particularly Support Vector Machines (SVM), to evaluate whether robot configurations are collision free, an operation termed ``collision detection''. Despite the growing popularity of these methods, there is a lack of theory supporting their efficiency and prediction accuracy. This is in stark contrast to the rich theoretical results of machine-learning methods in general and of SVMs in particular. Our work bridges this gap by analyzing the sample complexity of an SVM classifier for learning-based collision detection in motion planning. We bound the number of samples needed to achieve a specified accuracy at a given confidence level. This result is stated in terms relevant to robot motion-planning such as the system's clearance. Building on these theoretical results, we propose a collision-detection algorithm that can also provide statistical guarantees on the algorithm's error in classifying robot configurations as collision-free or not.