Frank-Wolfe Optimization for Dominant Set Clustering

We study Frank-Wolfe algorithms -- standard, pairwise, and away-steps -- for efficient optimization of Dominant Set Clustering. We present a unified and computationally efficient framework to employ the different variants of Frank-Wolfe methods, and we investigate its effectiveness via several experimental studies. In addition, we provide explicit convergence rates for the algorithms in terms of the so-called Frank-Wolfe gap. The theoretical analysis has been specialized to the problem of Dominant Set Clustering and is thus more easily accessible compared to prior work.

Memory-Efficient Sampling for Minimax Distance Measures

Minimax distance measure extracts the underlying patterns and manifolds in an unsupervised manner. The existing methods require a quadratic memory with respect to the number of objects. In this paper, we investigate efficient sampling schemes in order to reduce the memory requirement and provide a linear space complexity. In particular, we propose a novel sampling technique that adapts well with Minimax distances. We evaluate the methods on real-world datasets from different domains and analyze the results.

On the Unreasonable Effectiveness of Knowledge Distillation: Analysis in the Kernel Regime

Knowledge distillation (KD), i.e. one classifier being trained on the outputs of another classifier, is an empirically very successful technique for knowledge transfer between classifiers. It has even been observed that classifiers learn much faster and more reliably if trained with the outputs of another classifier as soft labels, instead of from ground truth data. However, there has been little or no theoretical analysis of this phenomenon. We provide the first theoretical analysis of KD in the setting of extremely wide two layer non-linear networks in model and regime in (Arora et al., 2019; Du & Hu, 2019; Cao & Gu, 2019). We prove results on what the student network learns and on the rate of convergence for the student network. Intriguingly, we also confirm the lottery ticket hypothesis (Frankle & Carbin, 2019) in this model. To prove our results, we extend the repertoire of techniques from linear systems dynamics. We give corresponding experimental analysis that validates the theoretical results and yields additional insights.

Convolutional Spiking Neural Networks for Spatio-Temporal Feature Extraction

Spiking neural networks (SNNs) can be used in low-power and embedded systems (such as emerging neuromorphic chips) due to their event-based nature. Also, they have the advantage of low computation cost in contrast to conventional artificial neural networks (ANNs), while preserving ANN's properties. However, temporal coding in layers of convolutional spiking neural networks and other types of SNNs has yet to be studied. In this paper, we provide insight into spatio-temporal feature extraction of convolutional SNNs in experiments designed to exploit this property. Our proposed shallow convolutional SNN outperforms state-of-the-art spatio-temporal feature extractor methods such as C3D, ConvLstm, and similar networks. Furthermore, we present a new deep spiking architecture to tackle real-world problems (in particular classification tasks), and the model achieved superior performance compared to other SNN methods on CIFAR10-DVS. It is also worth noting that the training process is implemented based on spatio-temporal backpropagation, and ANN to SNN conversion methods will serve no use.

An Online Learning Framework for Energy-Efficient Navigation of Electric Vehicles

Energy-efficient navigation constitutes an important challenge in electric vehicles, due to their limited battery capacity. We employ a Bayesian approach to model energy consumption at road-segments for efficient navigation. In order to learn the model parameters, we develop an online learning framework and investigate several exploration strategies such as Thompson Sampling and Upper Confidence Bound. We then extend our online learning framework to multi-agent setting, where multiple vehicles adaptively navigate and learn the parameters of the energy model. We analyze Thompson Sampling and establish rigorous regret bounds on its performance. Finally, we demonstrate the performance of our methods via several real-world experiments on Luxembourg SUMO Traffic dataset.

Hierarchical Correlation Clustering and Tree Preserving Embedding

We propose a hierarchical correlation clustering method that extends the well-known correlation clustering to produce hierarchical clusters. We then investigate embedding the respective hierarchy to be used for (tree preserving) embedding and feature extraction. We study the connection of such an embedding to single linkage embedding and minimax distances, and in particular study minimax distances for correlation clustering. Finally, we demonstrate the performance of our methods on several UCI and 20 newsgroup datasets.

Lifelong Learning Starting From Zero

We present a deep neural-network model for lifelong learning inspired by several forms of neuroplasticity. The neural network develops continuously in response to signals from the environment. In the beginning, the network is a blank slate with no nodes at all. It develops according to four rules: (i) expansion, which adds new nodes to memorize new input combinations; (ii) generalization, which adds new nodes that generalize from existing ones; (iii) forgetting, which removes nodes that are of relatively little use; and (iv) backpropagation, which fine-tunes the network parameters. We analyze the model from the perspective of accuracy, energy efficiency, and versatility and compare it to other network models, finding better performance in several cases.

Spectral Analysis of Kernel and Neural Embeddings: Optimization and Generalization

We extend the recent results of (Arora et al., 2019) by a spectral analysis of representations corresponding to kernel and neural embeddings. They showed that in a simple single layer network, the alignment of the labels to the eigenvectors of the corresponding Gram matrix determines both the convergence of the optimization during training as well as the generalization properties. We show quantitatively that kernel and neural representations improve both optimization and generalization. We give results for the Gaussian kernel and approximations by random Fourier features as well as for embeddings produced by two layer networks trained on different tasks.

Nonparametric feature extraction based on Minimax distance

We investigate the use of Minimax distances to extract in a nonparametric way the features that capture the unknown underlying patterns and structures in the data. We develop a general-purpose framework to employ Minimax distances with many machine learning methods that perform on numerical data. For this purpose, first, we compute the pairwise Minimax distances between the objects, using the equivalence of Minimax distances over a graph and over a minimum spanning tree constructed on that. Then, we perform an embedding of the pairwise Minimax distances into a new vector space, such that their squared Euclidean distances in the new space equal to the pairwise Minimax distances in the original space. In the following, we study the case of having multiple pairwise Minimax matrices, instead of a single one. Thereby, we propose an embedding via first summing up the centered matrices and then performing an eigenvalue decomposition. Finally, we perform several experimental studies to illustrate the effectiveness of our framework.

Trip Prediction by Leveraging Trip Histories from Neighboring Users

We propose a novel approach for trip prediction by analyzing user's trip histories. We augment users' (self-) trip histories by adding 'similar' trips from other users, which could be informative and useful for predicting future trips for a given user. This also helps to cope with noisy or sparse trip histories, where the self-history by itself does not provide a reliable prediction of future trips. We show empirical evidence that by enriching the users' trip histories with additional trips, one can improve the prediction error by 15%-40%, evaluated on multiple subsets of the Nancy2012 dataset. This real-world dataset is collected from public transportation ticket validations in the city of Nancy, France. Our prediction tool is a central component of a trip simulator system designed to analyze the functionality of public transportation in the city of Nancy.