Benjamin Letham

Interpretable classifiers using rules and Bayesian analysis: Building a better stroke prediction model

We aim to produce predictive models that are not only accurate, but are also interpretable to human experts. Our models are decision lists, which consist of a series of if...then... statements (e.g., if high blood pressure, then stroke) that discretize a high-dimensional, multivariate feature space into a series of simple, readily interpretable decision statements. We introduce a generative model called Bayesian Rule Lists that yields a posterior distribution over possible decision lists. It employs a novel prior structure to encourage sparsity. Our experiments show that Bayesian Rule Lists has predictive accuracy on par with the current top algorithms for prediction in machine learning. Our method is motivated by recent developments in personalized medicine, and can be used to produce highly accurate and interpretable medical scoring systems. We demonstrate this by producing an alternative to the CHADS

Onset timing of cross‐sensory activations and multisensory interactions in auditory and visual sensory cortices

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Sequential event prediction

score, actively used in clinical practice for estimating the risk of stroke in patients that have atrial fibrillation. Our model is as interpretable as CHADS

Growing a list

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Bayesian Inference of Arrival Rate and Substitution Behavior from Sales Transaction Data with Stockouts

, but more accurate.

A Computational Model of Inhibition of HIV-1 by Interferon-Alpha

Here we report early cross‐sensory activations and audiovisual interactions at the visual and auditory cortices using magnetoencephalography (MEG) to obtain accurate timing information. Data from an identical fMRI experiment were employed to support MEG source localization results. Simple auditory and visual stimuli (300‐ms noise bursts and checkerboards) were presented to seven healthy humans. MEG source analysis suggested generators in the auditory and visual sensory cortices for both within‐modality and cross‐sensory activations. fMRI cross‐sensory activations were strong in the visual but almost absent in the auditory cortex; this discrepancy with MEG possibly reflects the influence of acoustical scanner noise in fMRI. In the primary auditory cortices (Heschl’s gyrus) the onset of activity to auditory stimuli was observed at 23 ms in both hemispheres, and to visual stimuli at 82 ms in the left and at 75 ms in the right hemisphere. In the primary visual cortex (Calcarine fissure) the activations to visual stimuli started at 43 ms and to auditory stimuli at 53 ms. Cross‐sensory activations thus started later than sensory‐specific activations, by 55 ms in the auditory cortex and by 10 ms in the visual cortex, suggesting that the origins of the cross‐sensory activations may be in the primary sensory cortices of the opposite modality, with conduction delays (from one sensory cortex to another) of 30–35 ms. Audiovisual interactions started at 85 ms in the left auditory, 80 ms in the right auditory and 74 ms in the visual cortex, i.e., 3–21 ms after inputs from the two modalities converged.

Prediction uncertainty and optimal experimental design for learning dynamical systems.

In sequential event prediction, we are given a “sequence database” of past event sequences to learn from, and we aim to predict the next event within a current event sequence. We focus on applications where the set of the past events has predictive power and not the specific order of those past events. Such applications arise in recommender systems, equipment maintenance, medical informatics, and in other domains. Our formalization of sequential event prediction draws on ideas from supervised ranking. We show how specific choices within this approach lead to different sequential event prediction problems and algorithms. In recommender system applications, the observed sequence of events depends on user choices, which may be influenced by the recommendations, which are themselves tailored to the user’s choices. This leads to sequential event prediction algorithms involving a non-convex optimization problem. We apply our approach to an online grocery store recommender system, email recipient recommendation, and a novel application in the health event prediction domain.

Sequential Event Prediction with Association Rules

It is easy to find expert knowledge on the Internet on almost any topic, but obtaining a complete overview of a given topic is not always easy: information can be scattered across many sources and must be aggregated to be useful. We introduce a method for intelligently growing a list of relevant items, starting from a small seed of examples. Our algorithm takes advantage of the wisdom of the crowd, in the sense that there are many experts who post lists of things on the Internet. We use a collection of simple machine learning components to find these experts and aggregate their lists to produce a single complete and meaningful list. We use experiments with gold standards and open-ended experiments without gold standards to show that our method significantly outperforms the state of the art. Our method uses the ranking algorithm Bayesian Sets even when its underlying independence assumption is violated, and we provide a theoretical generalization bound to motivate its use.

An interpretable stroke prediction model using rules and Bayesian analysis

When an item goes out of stock, sales transaction data no longer reflect the original customer demand, since some customers leave with no purchase while others substitute alternative products for the one that was out of stock. Here we develop a Bayesian hierarchical model for inferring the underlying customer arrival rate and choice model from sales transaction data and the corresponding stock levels. The model uses a nonhomogeneous Poisson process to allow the arrival rate to vary throughout the day, and allows for a variety of choice models. Model parameters are inferred using a stochastic gradient MCMC algorithm that can scale to large transaction databases. We fit the model to data from a local bakery and show that it is able to make accurate out-of-sample predictions, and to provide actionable insight into lost cookie sales.

Learning theory analysis for association rules and sequential event prediction

Type 1 interferons such as interferon-alpha (IFNα) inhibit replication of Human immunodeficiency virus (HIV-1) by upregulating the expression of genes that interfere with specific steps in the viral life cycle. This pathway thus represents a potential target for immune-based therapies that can alter the dynamics of host-virus interactions to benefit the host. To obtain a deeper mechanistic understanding of how IFNα impacts spreading HIV-1 infection, we modeled the interaction of HIV-1 with CD4 T cells and IFNα as a dynamical system. This model was then tested using experimental data from a cell culture model of spreading HIV-1 infection. We found that a model in which IFNα induces reversible cellular states that block both early and late stages of HIV-1 infection, combined with a saturating rate of conversion to these states, was able to successfully fit the experimental dataset. Sensitivity analysis showed that the potency of inhibition by IFNα was particularly dependent on specific network parameters and rate constants. This model will be useful for designing new therapies targeting the IFNα network in HIV-1-infected individuals, as well as potentially serving as a template for understanding the interaction of IFNα with other viruses.