A Data-Driven State Aggregation Approach for Dynamic Discrete Choice Models

We study dynamic discrete choice models, where a commonly studied problem involves estimating parameters of agent reward functions (also known as "structural" parameters), using agent behavioral data. Maximum likelihood estimation for such models requires dynamic programming, which is limited by the curse of dimensionality. In this work, we present a novel algorithm that provides a data-driven method for selecting and aggregating states, which lowers the computational and sample complexity of estimation. Our method works in two stages. In the first stage, we use a flexible inverse reinforcement learning approach to estimate agent Q-functions. We use these estimated Q-functions, along with a clustering algorithm, to select a subset of states that are the most pivotal for driving changes in Q-functions. In the second stage, with these selected "aggregated" states, we conduct maximum likelihood estimation using a commonly used nested fixed-point algorithm. The proposed two-stage approach mitigates the curse of dimensionality by reducing the problem dimension. Theoretically, we derive finite-sample bounds on the associated estimation error, which also characterize the trade-off of computational complexity, estimation error, and sample complexity. We demonstrate the empirical performance of the algorithm in two classic dynamic discrete choice estimation applications

An Efficient Bandit Algorithm for Realtime Multivariate Optimization

Optimization is commonly employed to determine the content of web pages, such as to maximize conversions on landing pages or click-through rates on search engine result pages. Often the layout of these pages can be decoupled into several separate decisions. For example, the composition of a landing page may involve deciding which image to show, which wording to use, what color background to display, etc. Such optimization is a combinatorial problem over an exponentially large decision space. Randomized experiments do not scale well to this setting, and therefore, in practice, one is typically limited to optimizing a single aspect of a web page at a time. This represents a missed opportunity in both the speed of experimentation and the exploitation of possible interactions between layout decisions. Here we focus on multivariate optimization of interactive web pages. We formulate an approach where the possible interactions between different components of the page are modeled explicitly. We apply bandit methodology to explore the layout space efficiently and use hill-climbing to select optimal content in realtime. Our algorithm also extends to contextualization and personalization of layout selection. Simulation results show the suitability of our approach to large decision spaces with strong interactions between content. We further apply our algorithm to optimize a message that promotes adoption of an Amazon service. After only a single week of online optimization, we saw a 21% conversion increase compared to the median layout. Our technique is currently being deployed to optimize content across several locations at Amazon.com.Comment: KDD'17 Audience Appreciation Awar

Improved Confidence Bounds for the Linear Logistic Model and Applications to Linear Bandits

We propose improved fixed-design confidence bounds for the linear logistic model. Our bounds significantly improve upon the state-of-the-art bound by Li et al. (2017) via recent developments of the self-concordant analysis of the logistic loss (Faury et al., 2020). Specifically, our confidence bound avoids a direct dependence on $1/\kappa$, where $\kappa$ is the minimal variance over all arms' reward distributions. In general, $1/\kappa$ scales exponentially with the norm of the unknown linear parameter $\theta^*$. Instead of relying on this worst-case quantity, our confidence bound for the reward of any given arm depends directly on the variance of that arm's reward distribution. We present two applications of our novel bounds to pure exploration and regret minimization logistic bandits improving upon state-of-the-art performance guarantees. For pure exploration, we also provide a lower bound highlighting a dependence on $1/\kappa$ for a family of instances

Bayesian Meta-Prior Learning Using Empirical Bayes

Adding domain knowledge to a learning system is known to improve results. In multi-parameter Bayesian frameworks, such knowledge is incorporated as a prior. On the other hand, various model parameters can have different learning rates in real-world problems, especially with skewed data. Two often-faced challenges in Operation Management and Management Science applications are the absence of informative priors, and the inability to control parameter learning rates. In this study, we propose a hierarchical Empirical Bayes approach that addresses both challenges, and that can generalize to any Bayesian framework. Our method learns empirical meta-priors from the data itself and uses them to decouple the learning rates of first-order and second-order features (or any other given feature grouping) in a Generalized Linear Model. As the first-order features are likely to have a more pronounced effect on the outcome, focusing on learning first-order weights first is likely to improve performance and convergence time. Our Empirical Bayes method clamps features in each group together and uses the deployed model's observed data to empirically compute a hierarchical prior in hindsight. We report theoretical results for the unbiasedness, strong consistency, and optimal frequentist cumulative regret properties of our meta-prior variance estimator. We apply our method to a standard supervised learning optimization problem, as well as an online combinatorial optimization problem in a contextual bandit setting implemented in an Amazon production system. Both during simulations and live experiments, our method shows marked improvements, especially in cases of small traffic. Our findings are promising, as optimizing over sparse data is often a challenge.Comment: Expanded discussions on applications and extended literature review section. Forthcoming in the Management Science Journa

Predicting invasive breast cancer versus DCIS in different age groups.

BackgroundIncreasing focus on potentially unnecessary diagnosis and treatment of certain breast cancers prompted our investigation of whether clinical and mammographic features predictive of invasive breast cancer versus ductal carcinoma in situ (DCIS) differ by age.MethodsWe analyzed 1,475 malignant breast biopsies, 1,063 invasive and 412 DCIS, from 35,871 prospectively collected consecutive diagnostic mammograms interpreted at University of California, San Francisco between 1/6/1997 and 6/29/2007. We constructed three logistic regression models to predict the probability of invasive cancer versus DCIS for the following groups: women ≥ 65 (older group), women 50-64 (middle age group), and women < 50 (younger group). We identified significant predictors and measured the performance in all models using area under the receiver operating characteristic curve (AUC).ResultsThe models for older and the middle age groups performed significantly better than the model for younger group (AUC = 0.848 vs, 0.778; p = 0.049 and AUC = 0.851 vs, 0.778; p = 0.022, respectively). Palpability and principal mammographic finding were significant predictors in distinguishing invasive from DCIS in all age groups. Family history of breast cancer, mass shape and mass margins were significant positive predictors of invasive cancer in the older group whereas calcification distribution was a negative predictor of invasive cancer (i.e. predicted DCIS). In the middle age group--mass margins, and in the younger group--mass size were positive predictors of invasive cancer.ConclusionsClinical and mammographic finding features predict invasive breast cancer versus DCIS better in older women than younger women. Specific predictive variables differ based on age

Genetic Variants Improve Breast Cancer Risk Prediction on Mammograms

Several recent genome-wide association studies have identified genetic variants associated with breast cancer. However, how much these genetic variants may help advance breast cancer risk prediction based on other clinical features, like mammographic findings, is unknown. We conducted a retrospective case-control study, collecting mammographic findings and high-frequency/low-penetrance genetic variants from an existing personalized medicine data repository. A Bayesian network was developed using Tree Augmented Naive Bayes (TAN) by training on the mammographic findings, with and without the 22 genetic variants collected. We analyzed the predictive performance using the area under the ROC curve, and found that the genetic variants significantly improved breast cancer risk prediction on mammograms. We also identified the interaction effect between the genetic variants and collected mammographic findings in an attempt to link genotype to mammographic phenotype to better understand disease patterns, mechanisms, and/or natural history.