Yotam Hechtlinger

Yotam Hechtlinger, Barnabás Póczos, Larry Wasserman

Most classifiers operate by selecting the maximum of an estimate of the conditional distribution $p(y|x)$ where $x$ stands for the features of the instance to be classified and $y$ denotes its label. This often results in a {\em hubristic bias}: overconfidence in the assignment of a definite label. Usually, the observations are concentrated on a small volume but the classifier provides definite predictions for the entire space. We propose constructing conformal prediction sets which contain a set of labels rather than a single label. These conformal prediction sets contain the true label with probability $1-α$. Our construction is based on $p(x|y)$ rather than $p(y|x)$ which results in a classifier that is very cautious: it outputs the null set --- meaning "I don't know" --- when the object does not resemble the training examples. An important property of our approach is that adversarial attacks are likely to be predicted as the null set or would also include the true label. We demonstrate the performance on the ImageNet ILSVRC dataset and the CelebA and IMDB-Wiki facial datasets using high dimensional features obtained from state of the art convolutional neural networks.

Yotam Hechtlinger, Purvasha Chakravarti, Jining Qin

This paper introduces a generalization of Convolutional Neural Networks (CNNs) from low-dimensional grid data, such as images, to graph-structured data. We propose a novel spatial convolution utilizing a random walk to uncover the relations within the input, analogous to the way the standard convolution uses the spatial neighborhood of a pixel on the grid. The convolution has an intuitive interpretation, is efficient and scalable and can also be used on data with varying graph structure. Furthermore, this generalization can be applied to many standard regression or classification problems, by learning the the underlying graph. We empirically demonstrate the performance of the proposed CNN on MNIST, and challenge the state-of-the-art on Merck molecular activity data set.

Yotam Hechtlinger

State of the art machine learning algorithms are highly optimized to provide the optimal prediction possible, naturally resulting in complex models. While these models often outperform simpler more interpretable models by order of magnitudes, in terms of understanding the way the model functions, we are often facing a "black box". In this paper we suggest a simple method to interpret the behavior of any predictive model, both for regression and classification. Given a particular model, the information required to interpret it can be obtained by studying the partial derivatives of the model with respect to the input. We exemplify this insight by interpreting convolutional and multi-layer neural networks in the field of natural language processing.