We consider dynamic pricing with many products under an evolving but low-dimensional demand model. Assuming the temporal variation in cross-elasticities exhibits low-rank structure based on fixed (latent) features of the products, we show that the revenue maximization problem reduces to an online bandit convex optimization with side information given by the observed demands. We design dynamic pricing algorithms whose revenue approaches that of the best fixed price vector in hindsight, at a rate that only depends on the intrinsic rank of the demand model and not the number of products. Our approach applies a bandit convex optimization algorithm in a projected low-dimensional space spanned by the latent product features, while simultaneously learning this span via online singular value decomposition of a carefully-crafted matrix containing the observed demands.

Estimators computed from adaptively collected data do not behave like their non-adaptive brethren.Rather, the sequential dependence of the collection policy can lead to severe distributional biases that persist even in the infinite data limit. We develop a general method – $\mathbf{W}$-decorrelation – for transforming the bias of adaptive linear regression estimators into variance. The method uses only coarse-grained information about the data collection policy and does not need access to propensity scores or exact knowledge of the policy.We bound the finite-sample bias and variance of the $\mathbf{W}$-estimator and develop asymptotically correct confidence intervals based on a novel martingale central limit theorem. We then demonstrate the empirical benefits of the generic $\mathbf{W}$-decorrelation procedure in two different adaptive data settings: the multi-armed bandit and the autoregressive time series.

Counterfactual prediction requires understanding causal relationships between so-called treatment and outcome variables. This paper provides a recipe for augmenting deep learning methods to accurately characterize such relationships in the presence of instrument variables (IVs) – sources of treatment randomization that are conditionally independent from the outcomes. Our IV specification resolves into two prediction tasks that can be solved with deep neural nets: a first-stage network for treatment prediction and a second-stage network whose loss function involves integration over the conditional treatment distribution. This Deep IV framework allows us to take advantage of off-the-shelf supervised learning techniques to estimate causal effects by adapting the loss function. Experiments show that it outperforms existing machine learning approaches.

In order to match shoppers with desired products and provide personalized promotions, whether in online or offline shopping worlds, it is critical to model both consumer preferences and price sensitivities simultaneously. Personalized preferences have been thoroughly studied in the field of recommender systems, though price (and price sensitivity) has received relatively little attention. At the same time, price sensitivity has been richly explored in the area of economics, though typically not in the context of developing scalable, working systems to generate recommendations. In this study, we seek to bridge the gap between large-scale recommender systems and established consumer theories from economics, and propose a nested feature-based matrix factorization framework to model both preferences and price sensitivities. Quantitative and qualitative results indicate the proposed personalized, interpretable and scalable framework is capable of providing satisfying recommendations (on two datasets of grocery transactions) and can be applied to obtain economic insights into consumer behavior.

We derive ensembles of decision trees through a nonparametric Bayesian model, allowing us to view such ensembles as samples from a posterior distribution. This insight motivates a class of Bayesian Forest (BF) algorithms that provide small gains in performance and large gains in interpretability. Based on the BF framework, we are able to show that high-level tree hierarchy is stable in large samples. This motivates an empirical Bayesian Forest (EBF) algorithm for building approximate BFs on massive distributed datasets and we show that EBFs outperform sub-sampling based alternatives by a large margin.

Process models are widely used tools, both for studying fundamental processes themselves and as elements of larger system studies. A radiative transfer model (RTM) simulates the interaction of light with a medium. We are interested in RTMs that model light reflected from a vegetated region. Such an RTM takes as input various biospheric and illumination parameters and computes the upwelling radiation at the top of the canopy. The question we address is as follows: Which of the inputs to the RTM has the greatest impact on the computed observation? We study the leaf canopy model (LCM) RTM, which was designed to study the feasibility of observing leaf chemistry remotely. Its inputs are leaf chemistry variables (chlorophyll, water, lignin, and cellulose) and canopy structural parameters (leaf area index, leaf angle distribution, soil reflectance, and sun angle). We present a statistical approach to the sensitivity analysis of RTMs to answer the question previously posed. The focus is on global sensitivity analysis, studying how the RTM output changes as the inputs vary continuously according to a probability distribution over the input space. The influence of each input variable is captured through the “main effects” and “sensitivity indices.” Direct computation requires extensive computationally expensive runs of the RTM. We develop a Gaussian process approximation to the RTM output to enable efficient computation. We illustrate how the approach can effectively determine the inputs that are vital for accurate prediction. The methods are applied to the LCM with seven inputs and output obtained at eight wavelengths associated with Moderate-resolution Imaging Spectroradiometer bands that are sensitive to vegetation.