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Reproducible research in Machine Learning has seen a salutary abundance of progress lately: workflows, transparency, and statistical analysis of validation and test performance. We build on these efforts and take them further. We offer a principled experimental design methodology, based on linear mixed models, to study and separate the effects of multiple factors of variation in machine learning experiments. This approach allows to account for the effects of architecture, optimizer, hyper-parameters, intentional randomization, as well as unintended lack of determinism across reruns. We illustrate that methodology by analyzing Matching Networks, Prototypical Networks and TADAM on the miniImagenet dataset.
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Online controlled experiments are the primary tool for measuring the causal impact of product changes in digital businesses. It is increasingly common for digital products and services to interact with customers in a personalised way. Using online controlled experiments to optimise personalised interaction strategies is challenging because the usual assumption of statistically equivalent user groups is violated. Additionally, challenges are introduced by users qualifying for strategies based on dynamic, stochastic attributes. Traditional A/B tests can salvage statistical equivalence by pre-allocating users to control and exposed groups, but this dilutes the experimental metrics and reduces the test power. We present a stacked incrementality test framework that addresses problems with running online experiments for personalised user strategies. We derive bounds that show that our framework is superior to the best simple A/B test given enough users and that this condition is easily met for large scale online experiments. In addition, we provide a test power calculator and describe a selection of pitfalls and lessons learnt from our experience using it.
We consider Markov basis arising from fractional factorial designs with three-level factors. Once we have a Markov basis, $p$ values for various conditional tests are estimated by the Markov chain Monte Carlo procedure. For designed experiments with a single count observation for each run, we formulate a generalized linear model and consider a sample space with the same sufficient statistics to the observed data. Each model is characterized by a covariate matrix, which is constructed from the main and the interaction effects we intend to measure. We investigate fractional factorial designs with $3^{p-q}$ runs noting correspondences to the models for $3^{p-q}$ contingency tables.
How to measure the incremental Return On Ad Spend (iROAS) is a fundamental problem for the online advertising industry. A standard modern tool is to run randomized geo experiments, where experimental units are non-overlapping ad-targetable geographical areas (Vaver & Koehler 2011). However, how to design a reliable and cost-effective geo experiment can be complicated, for example: 1) the number of geos is often small, 2) the response metric (e.g. revenue) across geos can be very heavy-tailed due to geo heterogeneity, and furthermore 3) the response metric can vary dramatically over time. To address these issues, we propose a robust nonparametric method for the design, called Trimmed Match Design (TMD), which extends the idea of Trimmed Match (Chen & Au 2019) and furthermore integrates the techniques of optimal subset pairing and sample splitting in a novel and systematic manner. Some simulation and real case studies are presented. We also point out a few open problems for future research.
We review recent literature that proposes to adapt ideas from classical model based optimal design of experiments to problems of data selection of large datasets. Special attention is given to bias reduction and to protection against confounders. Some new results are presented. Theoretical and computational comparisons are made.
We study approaches to robust model-based design of experiments in the context of maximum-likelihood estimation. These approaches provide robustification of model-based methodologies for the design of optimal experiments by accounting for the effect of the parametric uncertainty. We study the problem of robust optimal design of experiments in the framework of nonlinear least-squares parameter estimation using linearized confidence regions. We investigate several well-known robustification frameworks in this respect and propose a novel methodology based on multi-stage robust optimization. The proposed methodology aims at problems, where the experiments are designed sequentially with a possibility of re-estimation in-between the experiments. The multi-stage formalism aids in identifying experiments that are better conducted in the early phase of experimentation, where parameter knowledge is poor. We demonstrate the findings and effectiveness of the proposed methodology using four case studies of varying complexity.
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