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Register a new userWhen Six Gates are Not Enough
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Added by
Peter Schneider-Kamp
Publication date
2015
fields
Informatics Engineering
and research's language is
English
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We apply the pigeonhole principle to show that there must exist Boolean functions on 7 inputs with a multiplicative complexity of at least 7, i.e., that cannot be computed with only 6 multiplications in the Galois field with two elements.
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Many structured prediction tasks in machine vision have a collection of acceptable answers, instead of one definitive ground truth answer. Segmentation of images, for example, is subject to human labeling bias. Similarly, there are multiple possible pixel values that could plausibly complete occluded image regions. State-of-the art supervised learning methods are typically optimized to make a single test-time prediction for each query, failing to find other modes in the output space. Existing methods that allow for sampling often sacrifice speed or accuracy. We introduce a simple method for training a neural network, which enables diverse structured predictions to be made for each test-time query. For a single input, we learn to predict a range of possible answers. We compare favorably to methods that seek diversity through an ensemble of networks. Such stochastic multiple choice learning faces mode collapse, where one or more ensemble members fail to receive any training signal. Our best performing solution can be deployed for various tasks, and just involves small modifications to the existing single-mode architecture, loss function, and training regime. We demonstrate that our method results in quantitative improvements across three challenging tasks: 2D image completion, 3D volume estimation, and flow prediction.
We argue that randomized controlled trials (RCTs) are special even among settings where average treatment effects are identified by a nonparametric unconfoundedness assumption. This claim follows from two results of Robins and Ritov (1997): (1) with at least one continuous covariate control, no estimator of the average treatment effect exists which is uniformly consistent without further assumptions, (2) knowledge of the propensity score yields a consistent estimator and confidence intervals at parametric rates, regardless of how complicated the propensity score function is. We emphasize the latter point, and note that successfully-conducted RCTs provide knowledge of the propensity score to the researcher. We discuss modern developments in covariate adjustment for RCTs, noting that statistical models and machine learning methods can be used to improve efficiency while preserving finite sample unbiasedness. We conclude that statistical inference has the potential to be fundamentally more difficult in observational settings than it is in RCTs, even when all confounders are measured.
Sparsity promoting regularization is an important technique for signal reconstruction and several other ill-posed problems. Theoretical investigation typically bases on the assumption that the unknown solution has a sparse representation with respect to a fixed basis. We drop this sparsity assumption and provide error estimates for non-sparse solutions. After discussing a result in this direction published earlier by one of the authors and coauthors we prove a similar error estimate under weaker assumptions. Two examples illustrate that this set of weaker assumptions indeed covers additional situations which appear in applications.
In this work, we present a framework to measure and mitigate intrinsic biases with respect to protected variables --such as gender-- in visual recognition tasks. We show that trained models significantly amplify the association of target labels with gender beyond what one would expect from biased datasets. Surprisingly, we show that even when datasets are balanced such that each label co-occurs equally with each gender, learned models amplify the association between labels and gender, as much as if data had not been balanced! To mitigate this, we adopt an adversarial approach to remove unwanted features corresponding to protected variables from intermediate representations in a deep neural network -- and provide a detailed analysis of its effectiveness. Experiments on two datasets: the COCO dataset (objects), and the imSitu dataset (actions), show reductions in gender bias amplification while maintaining most of the accuracy of the original models.
We introduce uncertainty regions to perform inference on partial correlations when data are missing not at random. These uncertainty regions are shown to have a desired asymptotic coverage. Their finite sample performance is illustrated via simulations and real data example.
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