Solving Inverse Problems with Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity

A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the proposed framework with structured sparse estimation is described, which shows that the resulting piecewise linear estimate stabilizes the estimation when compared to traditional sparse inverse problem techniques. This interpretation also suggests an effective dictionary motivated initialization for the MAP-EM algorithm. We demonstrate that in a number of image inverse problems, including inpainting, zooming, and deblurring, the same algorithm produces either equal, often significantly better, or very small margin worse results than the best published ones, at a lower computational cost.Comment: 30 page

Multicriteria Analysis of Neural Network Forecasting Models: An Application to German Regional Labour Markets

This paper develops a flexible multi-dimensional assessment method for the comparison of different statistical-econometric techniques based on learning mechanisms with a view to analysing and forecasting regional labour markets. The aim of this paper is twofold. A first major objective is to explore the use of a standard choice tool, namely Multicriteria Analysis (MCA), in order to cope with the intrinsic methodological uncertainty on the choice of a suitable statistical-econometric learning technique for regional labour market analysis. MCA is applied here to support choices on the performance of various models -based on classes of Neural Network (NN) techniques-that serve to generate employment forecasts in West Germany at a regional/district level. A second objective of the paper is to analyse the methodological potential of a blend of approaches (NN-MCA) in order to extend the analysis framework to other economic research domains, where formal models are not available, but where a variety of statistical data is present. The paper offers a basis for a more balanced judgement of the performance of rival statistical tests

Are v1 simple cells optimized for visual occlusions? : A comparative study

Abstract: Simple cells in primary visual cortex were famously found to respond to low-level image components such as edges. Sparse coding and independent component analysis (ICA) emerged as the standard computational models for simple cell coding because they linked their receptive fields to the statistics of visual stimuli. However, a salient feature of image statistics, occlusions of image components, is not considered by these models. Here we ask if occlusions have an effect on the predicted shapes of simple cell receptive fields. We use a comparative approach to answer this question and investigate two models for simple cells: a standard linear model and an occlusive model. For both models we simultaneously estimate optimal receptive fields, sparsity and stimulus noise. The two models are identical except for their component superposition assumption. We find the image encoding and receptive fields predicted by the models to differ significantly. While both models predict many Gabor-like fields, the occlusive model predicts a much sparser encoding and high percentages of ‘globular’ receptive fields. This relatively new center-surround type of simple cell response is observed since reverse correlation is used in experimental studies. While high percentages of ‘globular’ fields can be obtained using specific choices of sparsity and overcompleteness in linear sparse coding, no or only low proportions are reported in the vast majority of studies on linear models (including all ICA models). Likewise, for the here investigated linear model and optimal sparsity, only low proportions of ‘globular’ fields are observed. In comparison, the occlusive model robustly infers high proportions and can match the experimentally observed high proportions of ‘globular’ fields well. Our computational study, therefore, suggests that ‘globular’ fields may be evidence for an optimal encoding of visual occlusions in primary visual cortex. Author Summary: The statistics of our visual world is dominated by occlusions. Almost every image processed by our brain consists of mutually occluding objects, animals and plants. Our visual cortex is optimized through evolution and throughout our lifespan for such stimuli. Yet, the standard computational models of primary visual processing do not consider occlusions. In this study, we ask what effects visual occlusions may have on predicted response properties of simple cells which are the first cortical processing units for images. Our results suggest that recently observed differences between experiments and predictions of the standard simple cell models can be attributed to occlusions. The most significant consequence of occlusions is the prediction of many cells sensitive to center-surround stimuli. Experimentally, large quantities of such cells are observed since new techniques (reverse correlation) are used. Without occlusions, they are only obtained for specific settings and none of the seminal studies (sparse coding, ICA) predicted such fields. In contrast, the new type of response naturally emerges as soon as occlusions are considered. In comparison with recent in vivo experiments we find that occlusive models are consistent with the high percentages of center-surround simple cells observed in macaque monkeys, ferrets and mice

Multi-round Master-Worker Computing: a Repeated Game Approach

We consider a computing system where a master processor assigns tasks for execution to worker processors through the Internet. We model the workers decision of whether to comply (compute the task) or not (return a bogus result to save the computation cost) as a mixed extension of a strategic game among workers. That is, we assume that workers are rational in a game-theoretic sense, and that they randomize their strategic choice. Workers are assigned multiple tasks in subsequent rounds. We model the system as an infinitely repeated game of the mixed extension of the strategic game. In each round, the master decides stochastically whether to accept the answer of the majority or verify the answers received, at some cost. Incentives and/or penalties are applied to workers accordingly. Under the above framework, we study the conditions in which the master can reliably obtain tasks results, exploiting that the repeated games model captures the effect of long-term interaction. That is, workers take into account that their behavior in one computation will have an effect on the behavior of other workers in the future. Indeed, should a worker be found to deviate from some agreed strategic choice, the remaining workers would change their own strategy to penalize the deviator. Hence, being rational, workers do not deviate. We identify analytically the parameter conditions to induce a desired worker behavior, and we evaluate experi- mentally the mechanisms derived from such conditions. We also compare the performance of our mechanisms with a previously known multi-round mechanism based on reinforcement learning.Comment: 21 pages, 3 figure

Ithemal: Accurate, Portable and Fast Basic Block Throughput Estimation using Deep Neural Networks

Predicting the number of clock cycles a processor takes to execute a block of assembly instructions in steady state (the throughput) is important for both compiler designers and performance engineers. Building an analytical model to do so is especially complicated in modern x86-64 Complex Instruction Set Computer (CISC) machines with sophisticated processor microarchitectures in that it is tedious, error prone, and must be performed from scratch for each processor generation. In this paper we present Ithemal, the first tool which learns to predict the throughput of a set of instructions. Ithemal uses a hierarchical LSTM--based approach to predict throughput based on the opcodes and operands of instructions in a basic block. We show that Ithemal is more accurate than state-of-the-art hand-written tools currently used in compiler backends and static machine code analyzers. In particular, our model has less than half the error of state-of-the-art analytical models (LLVM's llvm-mca and Intel's IACA). Ithemal is also able to predict these throughput values just as fast as the aforementioned tools, and is easily ported across a variety of processor microarchitectures with minimal developer effort.Comment: Published at 36th International Conference on Machine Learning (ICML) 201