**Best Linear Unbiased Estimator (BLUE)**

In statistics, the Gauss-Markov theorem, named after Carl Friedrich Gauss and Andrey Markov, states that in a linear regression model in which the errors have expectation zero and are uncorrelated and have equal variances, the best linear unbiased estimator (BLUE) of the coefficients is given by the ordinary least squares (OLS) estimator. Here ‘best’ means giving the lowest variance of the estimate, as compared to other unbiased, linear estimators. The errors don’t need to be normal, nor do they need to be independent and identically distributed (only uncorrelated and homoscedastic). The hypothesis that the estimator be unbiased cannot be dropped, since otherwise estimators better than OLS exist. See for examples the James-Stein estimator (which also drops linearity) or ridge regression.

➘ “Gauss-Markov Theorem” … **Myia**

We review the current state of automatic differentiation (AD) for array programming in machine learning (ML), including the different approaches such as operator overloading (OO) and source transformation (ST) used for AD, graph-based intermediate representations for programs, and source languages. Based on these insights, we introduce a new graph-based intermediate representation (IR) which specifically aims to efficiently support fully-general AD for array programming. Unlike existing dataflow programming representations in ML frameworks, our IR naturally supports function calls, higher-order functions and recursion, making ML models easier to implement. The ability to represent closures allows us to perform AD using ST without a tape, making the resulting derivative (adjoint) program amenable to ahead-of-time optimization using tools from functional language compilers, and enabling higher-order derivatives. Lastly, we introduce a proof of concept compiler toolchain called Myia which uses a subset of Python as a front end. … **Compositional Pattern Producing Network (DPPN)**

Compositional pattern-producing networks (CPPNs) are a variation of artificial neural networks (ANNs) that differ in their set of activation functions and how they are applied. While ANNs often contain only sigmoid functions and sometimes Gaussian functions, CPPNs can include both types of functions and many others. The choice of functions for the canonical set can be biased toward specific types of patterns and regularities. For example, periodic functions such as sine produce segmented patterns with repetitions, while symmetric functions such as Gaussian produce symmetric patterns. Linear functions can be employed to produce linear or fractal-like patterns. Thus, the architect of a CPPN-based genetic art system can bias the types of patterns it generates by deciding the set of canonical functions to include. … **Active Scene Learning**

Sketch recognition allows natural and efficient interaction in pen-based interfaces. A key obstacle to building accurate sketch recognizers has been the difficulty of creating large amounts of annotated training data. Several authors have attempted to address this issue by creating synthetic data, and by building tools that support efficient annotation. Two prominent sets of approaches stand out from the rest of the crowd. They use interim classifiers trained with a small set of labeled data to aid the labeling of the remainder of the data. The first set of approaches uses a classifier trained with a partially labeled dataset to automatically label unlabeled instances. The others, based on active learning, save annotation effort by giving priority to labeling informative data instances. The former is sub-optimal since it doesn’t prioritize the order of labeling to favor informative instances, while the latter makes the strong assumption that unlabeled data comes in an already segmented form (i.e. the ink in the training data is already assembled into groups forming isolated object instances). In this paper, we propose an active learning framework that combines the strengths of these methods, while addressing their weaknesses. In particular, we propose two methods for deciding how batches of unsegmented sketch scenes should be labeled. The first method, scene-wise selection, assesses the informativeness of each drawing (sketch scene) as a whole, and asks the user to annotate all objects in the drawing. The latter, segment-wise selection, attempts more precise targeting to locate informative fragments of drawings for user labeling. We show that both selection schemes outperform random selection. Furthermore, we demonstrate that precise targeting yields superior performance. Overall, our approach allows reaching top accuracy figures with up to 30% savings in annotation cost. …

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