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Register a new userUplift Modeling for Multiple Treatments with Cost Optimization
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Uplift modeling is an emerging machine learning approach for estimating the treatment effect at an individual or subgroup level. It can be used for optimizing the performance of interventions such as marketing campaigns and product designs. Uplift modeling can be used to estimate which users are likely to benefit from a treatment and then prioritize delivering or promoting the preferred experience to those users. An important but so far neglected use case for uplift modeling is an experiment with multiple treatment groups that have different costs, such as for example when different communication channels and promotion types are tested simultaneously. In this paper, we extend standard uplift models to support multiple treatment groups with different costs. We evaluate the performance of the proposed models using both synthetic and real data. We also describe a production implementation of the approach.
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The Hilbert Schmidt Independence Criterion (HSIC) is a kernel dependence measure that has applications in various aspects of machine learning. Conveniently, the objectives of different dimensionality reduction applications using HSIC often reduce to the same optimization problem. However, the nonconvexity of the objective function arising from non-linear kernels poses a serious challenge to optimization efficiency and limits the potential of HSIC-based formulations. As a result, only linear kernels have been computationally tractable in practice. This paper proposes a spectral-based optimization algorithm that extends beyond the linear kernel. The algorithm identifies a family of suitable kernels and provides the first and second-order local guarantees when a fixed point is reached. Furthermore, we propose a principled initialization strategy, thereby removing the need to repeat the algorithm at random initialization points. Compared to state-of-the-art optimization algorithms, our empirical results on real data show a run-time improvement by as much as a factor of $10^5$ while consistently achieving lower cost and classification/clustering errors. The implementation source code is publicly available on https://github.com/endsley.
The autoencoder model uses an encoder to map data samples to a lower dimensional latent space and then a decoder to map the latent space representations back to the data space. Implicitly, it relies on the encoder to approximate the inverse of the decoder network, so that samples can be mapped to and back from the latent space faithfully. This approximation may lead to sub-optimal latent space representations. In this work, we investigate a decoder-only method that uses gradient flow to encode data samples in the latent space. The gradient flow is defined based on a given decoder and aims to find the optimal latent space representation for any given sample through optimisation, eliminating the need of an approximate inversion through an encoder. Implementing gradient flow through ordinary differential equations (ODE), we leverage the adjoint method to train a given decoder. We further show empirically that the costly integrals in the adjoint method may not be entirely necessary. Additionally, we propose a $2^{nd}$ order ODE variant to the method, which approximates Nesterovs accelerated gradient descent, with faster convergence per iteration. Commonly used ODE solvers can be quite sensitive to the integration step-size depending on the stiffness of the ODE. To overcome the sensitivity for gradient flow encoding, we use an adaptive solver that prioritises minimising loss at each integration step. We assess the proposed method in comparison to the autoencoding model. In our experiments, GFE showed a much higher data-efficiency than the autoencoding model, which can be crucial for data scarce applications.
Data-driven pricing strategies are becoming increasingly common, where customers are offered a personalized price based on features that are predictive of their valuation of a product. It is desirable for this pricing policy to be simple and interpretable, so it can be verified, checked for fairness, and easily implemented. However, efforts to incorporate machine learning into a pricing framework often lead to complex pricing policies which are not interpretable, resulting in slow adoption in practice. We present a customized, prescriptive tree-based algorithm that distills knowledge from a complex black-box machine learning algorithm, segments customers with similar valuations and prescribes prices in such a way that maximizes revenue while maintaining interpretability. We quantify the regret of a resulting policy and demonstrate its efficacy in applications with both synthetic and real-world datasets.
In this paper, we introduce a novel task for machine learning in healthcare, namely personalized modeling of the female hormonal cycle. The motivation for this work is to model the hormonal cycle and predict its phases in time, both for healthy individuals and for those with disorders of the reproductive system. Because there are individual differences in the menstrual cycle, we are particularly interested in personalized models that can account for individual idiosyncracies, towards identifying phenotypes of menstrual cycles. As a first step, we consider the hormonal cycle as a set of observations through time. We use a previously validated mechanistic model to generate realistic hormonal patterns, and experiment with Gaussian process regression to estimate their values over time. Specifically, we are interested in the feasibility of predicting menstrual cycle phases under varying learning conditions: number of cycles used for training, hormonal measurement noise and sampling rates, and informed vs. agnostic sampling of hormonal measurements. Our results indicate that Gaussian processes can help model the female menstrual cycle. We discuss the implications of our experiments in the context of modeling the female menstrual cycle.
Uplift modeling is a predictive modeling technique that estimates the user-level incremental effect of a treatment using machine learning models. It is often used for targeting promotions and advertisements, as well as for the personalization of product offerings. In these applications, there are often hundreds of features available to build such models. Keeping all the features in a model can be costly and inefficient. Feature selection is an essential step in the modeling process for multiple reasons: improving the estimation accuracy by eliminating irrelevant features, accelerating model training and prediction speed, reducing the monitoring and maintenance workload for feature data pipeline, and providing better model interpretation and diagnostics capability. However, feature selection methods for uplift modeling have been rarely discussed in the literature. Although there are various feature selection methods for standard machine learning models, we will demonstrate that those methods are sub-optimal for solving the feature selection problem for uplift modeling. To address this problem, we introduce a set of feature selection methods designed specifically for uplift modeling, including both filter methods and embedded methods. To evaluate the effectiveness of the proposed feature selection methods, we use different uplift models and measure the accuracy of each model with a different number of selected features. We use both synthetic and real data to conduct these experiments. We also implemented the proposed filter methods in an open source Python package (CausalML).
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