Improving Generalization by Controlling Label-Noise Information in Neural Network Weights

In the presence of noisy or incorrect labels, neural networks have the undesirable tendency to memorize information about the noise. Standard regularization techniques such as dropout, weight decay or data augmentation sometimes help, but do not prevent this behavior. If one considers neural network weights as random variables that depend on the data and stochasticity of training, the amount of memorized information can be quantified with the Shannon mutual information between weights and the vector of all training labels given inputs, $I(w : \mathbf{y} \mid \mathbf{x})$. We show that for any training algorithm, low values of this term correspond to reduction in memorization of label-noise and better generalization bounds. To obtain these low values, we propose training algorithms that employ an auxiliary network that predicts gradients in the final layers of a classifier without accessing labels. We illustrate the effectiveness of our approach on versions of MNIST, CIFAR-10, and CIFAR-100 corrupted with various noise models, and on a large-scale dataset Clothing1M that has noisy labels.

Anchored Correlation Explanation: Topic Modeling with Minimal Domain Knowledge

While generative models such as Latent Dirichlet Allocation (LDA) have proven fruitful in topic modeling, they often require detailed assumptions and careful specification of hyperparameters. Such model complexity issues only compound when trying to generalize generative models to incorporate human input. We introduce Correlation Explanation (CorEx), an alternative approach to topic modeling that does not assume an underlying generative model, and instead learns maximally informative topics through an information-theoretic framework. This framework naturally generalizes to hierarchical and semi-supervised extensions with no additional modeling assumptions. In particular, word-level domain knowledge can be flexibly incorporated within CorEx through anchor words, allowing topic separability and representation to be promoted with minimal human intervention. Across a variety of datasets, metrics, and experiments, we demonstrate that CorEx produces topics that are comparable in quality to those produced by unsupervised and semi-supervised variants of LDA.

Sifting Common Information from Many Variables

Measuring the relationship between any pair of variables is a rich and active area of research that is central to scientific practice. In contrast, characterizing the common information among any group of variables is typically a theoretical exercise with few practical methods for high-dimensional data. A promising solution would be a multivariate generalization of the famous Wyner common information, but this approach relies on solving an apparently intractable optimization problem. We leverage the recently introduced information sieve decomposition to formulate an incremental version of the common information problem that admits a simple fixed point solution, fast convergence, and complexity that is linear in the number of variables. This scalable approach allows us to demonstrate the usefulness of common information in high-dimensional learning problems. The sieve outperforms standard methods on dimensionality reduction tasks, solves a blind source separation problem that cannot be solved with ICA, and accurately recovers structure in brain imaging data.

Toward Interpretable Topic Discovery via Anchored Correlation Explanation

Many predictive tasks, such as diagnosing a patient based on their medical chart, are ultimately defined by the decisions of human experts. Unfortunately, encoding experts' knowledge is often time consuming and expensive. We propose a simple way to use fuzzy and informal knowledge from experts to guide discovery of interpretable latent topics in text. The underlying intuition of our approach is that latent factors should be informative about both correlations in the data and a set of relevance variables specified by an expert. Mathematically, this approach is a combination of the information bottleneck and Total Correlation Explanation (CorEx). We give a preliminary evaluation of Anchored CorEx, showing that it produces more coherent and interpretable topics on two distinct corpora.