We investigate the optimal design of experimental studies that have pre-treatment outcome data available. The average treatment effect is estimated as the difference between the weighted average outcomes of the treated and control units. A number of commonly used approaches fit this formulation, including the difference-inmeans estimator and a variety of synthetic-control techniques. We propose several methods for choosing the set of treated units in conjunction with the weights. Observing the NP-hardness of the problem, we introduce a mixed-integer programming formulation which selects both the treatment and control sets and unit weightings. We prove that these proposed approaches lead to qualitatively different experimental units being selected for treatment. We use simulations based on publicly available data from the USBureau of Labor Statistics that show improvements in terms of mean squared error and statistical power when compared to simple and commonly used alternatives such as randomized trials.

In this material, we will give more technical details as well as additional experiments to support the main paper. The overview of the proposed framework, DeWave, is illustrated in Figure 6. Ground Bush attended the University of Texas at Austin, where he graduated Phi Beta Kappa with a Truth Bachelor's degree in Latin American Studies in 1973, taking only two and a half years to complete his work, and obtaining generally excellent grades. Predictwas the University of California at Austin in where he studied in Beta Kappa in a degree of degree in history American Studies in 1975. ZuCo stands for Zurich Cognitive Language Processing Corpus (ZuCo), a dataset that includes both raw and preprocessed eye-tracking and electroencephalography (EEG) data. The data is collected by having human subjects read given text corpora while simultaneously recording both their eye-tracking signals and EEG waves.

Work in deep clustering focuses on finding a single partition of data.

In recent years, Bi-Level Optimization (BLO) techniques have received extensive attentions from both learning and vision communities. A variety of BLO models in complex and practical tasks are of non-convex follower structure in nature (a.k.a., without Lower-Level Convexity, LLC for short). However, this challenging class of BLOs is lack of developments on both efficient solution strategies and solid theoretical guarantees. In this work, we propose a new algorithmic framework, named Initialization Auxiliary and Pessimistic Trajectory Truncated Gradient Method (IAPTT-GM), to partially address the above issues. In particular, by introducing an auxiliary as initialization to guide the optimization dynamics and designing a pessimistic trajectory truncation operation, we construct a reliable approximate version of the original BLO in the absence of LLC hypothesis. Our theoretical investigations establish the convergence of solutions returned by IAPTT-GM towards those of the original BLO without LLC. As an additional bonus, we also theoretically justify the quality of our IAPTT-GM embedded with Nesterov's accelerated dynamics under LLC. The experimental results confirm both the convergence of our algorithm without LLC, and the theoretical findings under LLC.

We consider the problem of variance reduction in randomized controlled trials, through the use of covariates correlated with the outcome but independent of the treatment. We propose a machine learning regression-adjusted treatment effect estimator, which we call MLRATE. MLRATE uses machine learning predictors of the outcome to reduce estimator variance. It employs cross-fitting to avoid overfitting biases, and we prove consistency and asymptotic normality under general conditions. MLRATE is robust to poor predictions from the machine learning step: if the predictions are uncorrelated with the outcomes, the estimator performs asymptotically no worse than the standard difference-in-means estimator, while if predictions are highly correlated with outcomes, the efficiency gains are large. In A/A tests, for a set of 48 outcome metrics commonly monitored in Facebook experiments the estimator has over 70% lower variance than the simple differencein-means estimator, and about 19% lower variance than the common univariate procedure which adjusts only for pre-experiment values of the outcome.

RELU networks have remained the default choice for models in the area of image prediction despite their well-established spectral bias towards learning low frequencies faster, and consequently their difficulty of reproducing high frequency visual details. As an alternative, sinnetworks showed promising results in learning implicit representations of visual data. However training these networks in practically relevant settings proved to be difficult, requiring careful initialization, dealing with issues due to inconsistent gradients, and a degeneracy in local minima. In this work, we instead propose replacing a baseline network's existing activations with a novel ensemble function with trainable parameters. The proposed METASIN activation can be trained reliably without requiring intricate initialization schemes, and results in consistently lower test loss compared to alternatives. We demonstrate our method in the areas of Monte-Carlo denoising and image resampling where we set new state-of-the-art through a knowledge distillation based training procedure. We present ablations on hyper-parameter settings, comparisons with alternative activation function formulations, and discuss the use of our method in other domains, such as image classification.

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