Robust Model Compression Using Deep Hypotheses

Machine Learning models should ideally be compact and robust. Compactness provides efficiency and comprehensibility whereas robustness provides resilience. Both topics have been studied in recent years but in isolation. Here we present a robust model compression scheme which is independent of model types: it can compress ensembles, neural networks and other types of models into diverse types of small models. The main building block is the notion of depth derived from robust statistics. Originally, depth was introduced as a measure of the centrality of a point in a sample such that the median is the deepest point. This concept was extended to classification functions which makes it possible to define the depth of a hypothesis and the median hypothesis. Algorithms have been suggested to approximate the median but they have been limited to binary classification. In this study, we present a new algorithm, the Multiclass Empirical Median Optimization (MEMO) algorithm that finds a deep hypothesis in multi-class tasks, and prove its correctness. This leads to our Compact Robust Estimated Median Belief Optimization (CREMBO) algorithm for robust model compression. We demonstrate the success of this algorithm empirically by compressing neural networks and random forests into small decision trees, which are interpretable models, and show that they are more accurate and robust than other comparable methods. In addition, our empirical study shows that our method outperforms Knowledge Distillation on DNN to DNN compression

Graph Trees with Attention

When dealing with tabular data, models based on regression and decision trees are a popular choice due to the high accuracy they provide on such tasks and their ease of application as compared to other model classes. Yet, when it comes to graph-structure data, current tree learning algorithms do not provide tools to manage the structure of the data other than relying on feature engineering. In this work we address the above gap, and introduce Graph Trees with Attention (GTA), a new family of tree-based learning algorithms that are designed to operate on graphs. GTA leverages both the graph structure and the features at the vertices and employs an attention mechanism that allows decisions to concentrate on sub-structures of the graph. We analyze GTA models and show that they are strictly more expressive than plain decision trees. We also demonstrate the benefits of GTA empirically on multiple graph and node prediction benchmarks. In these experiments, GTA always outperformed other tree-based models and often outperformed other types of graph-learning algorithms such as Graph Neural Networks (GNNs) and Graph Kernels. Finally, we also provide an explainability mechanism for GTA, and demonstrate it can provide intuitive explanations

Large Scale and Streaming Time Series Segmentation and Piece-Wise Approximation Extended Version

Abstract Segmenting a time series or approximating it with piecewise linear function is often needed when handling data in the time domain to detect outliers, clean data, detect events and more. The data varies from ECG signals, traffic monitors to stock prices and sensor networks. Modern data-sets of this type are large and in many cases are infinite in the sense that the data is a stream rather than a finite sample. Therefore, in order to segment it, an algorithm has to scale gracefully with the size of the data. Dynamic Programming (DP) can find the optimal segmentation, however, the DP approach has a complexity of O T 2 thus cannot handle datasets with millions of elements, nor can it handle streaming data. Therefore, various heuristics are used in practice to handle the data. This study shows that if the approximation measure has an inverse triangle inequality property (ITIP), the solution of the dynamic program can be computed in linear time and streaming data can be handled too. The ITIP is shown to hold in many cases of interest. The speedup due to the new algorithms is evaluated on a variety of data-sets to be in the range of 8 − 8200x over the DP solution without sacrificing accuracy. Confidence intervals for segmentations are derived as well

Graph Neural Networks Use Graphs When They Shouldn't

Predictions over graphs play a crucial role in various domains, including social networks, molecular biology, medicine, and more. Graph Neural Networks (GNNs) have emerged as the dominant approach for learning on graph data. Instances of graph labeling problems consist of the graph-structure (i.e., the adjacency matrix), along with node-specific feature vectors. In some cases, this graph-structure is non-informative for the predictive task. For instance, molecular properties such as molar mass depend solely on the constituent atoms (node features), and not on the molecular structure. While GNNs have the ability to ignore the graph-structure in such cases, it is not clear that they will. In this work, we show that GNNs actually tend to overfit the graph-structure in the sense that they use it even when a better solution can be obtained by ignoring it. We examine this phenomenon with respect to different graph distributions and find that regular graphs are more robust to this overfitting. We then provide a theoretical explanation for this phenomenon, via analyzing the implicit bias of gradient-descent-based learning of GNNs in this setting. Finally, based on our empirical and theoretical findings, we propose a graph-editing method to mitigate the tendency of GNNs to overfit graph-structures that should be ignored. We show that this method indeed improves the accuracy of GNNs across multiple benchmarks