**Xy**

Simulating Supervised Learning Data drawing . With Xy() you can convienently simulate regression data. The simulation can be very specific, since the user has many degrees of freedom. For instance, the functional shape and hence the polynomial degree of nonlinearity can be manipulated. Interaction can be formed and (co)variances altered. For a more specific motivation you can visit our blog … **Randomized Singular Value Decomposition (rSVD)**

Matrix completion is a widely used technique for image inpainting and personalized recommender system, etc. In this work, we focus on accelerating the matrix completion using faster randomized singular value decomposition (rSVD). Firstly, two fast randomized algorithms (rSVD-PI and rSVD- BKI) are proposed for handling sparse matrix. They make use of an eigSVD procedure and several accelerating skills. Then, with the rSVD-BKI algorithm and a new subspace recycling technique, we accelerate the singular value thresholding (SVT) method in [1] to realize faster matrix completion. Experiments show that the proposed rSVD algorithms can be 6X faster than the basic rSVD algorithm [2] while keeping same accuracy. For image inpainting and movie-rating estimation problems, the proposed accelerated SVT algorithm consumes 15X and 8X less CPU time than the methods using svds and lansvd respectively, without loss of accuracy. … **Tensor Monte Carlo**

Multi-sample objectives improve over single-sample estimates by giving tighter variational bounds and more accurate estimates of posterior uncertainty. However, these multi-sample techniques scale poorly, in the sense that the number of samples required to maintain the same quality of posterior approximation scales exponentially in the number of latent dimensions. One approach to addressing these issues is sequential Monte Carlo (SMC). However for many problems SMC is prohibitively slow because the resampling steps imposes an inherently sequential structure on the computation, which is difficult to effectively parallelise on GPU hardware. We developed tensor Monte-Carlo to address these issues. In particular, whereas the usual multi-sample objective draws $K$ samples from a joint distribution over all latent variables, we draw $K$ samples for each of the $n$ individual latent variables, and form our bound by averaging over all $K^n$ combinations of samples from each individual latent. While this sum over exponentially many terms might seem to be intractable, in many cases it can be efficiently computed by exploiting conditional independence structure. In particular, we generalise and simplify classical algorithms such as message passing by noting that these sums can be computed can be written in an extremely simple, general form: a series of tensor inner-products which can be depicted graphically as reductions of a factor graph. As such, we can straightforwardly combine summation over discrete variables with importance sampling over importance sampling over continuous variables. … **Memory-Efficient Convolution (MEC)**

Convolution is a critical component in modern deep neural networks, thus several algorithms for convolution have been developed. Direct convolution is simple but suffers from poor performance. As an alternative, multiple indirect methods have been proposed including im2col-based convolution, FFT-based convolution, or Winograd-based algorithm. However, all these indirect methods have high memory-overhead, which creates performance degradation and offers a poor trade-off between performance and memory consumption. In this work, we propose a memory-efficient convolution or MEC with compact lowering, which reduces memory-overhead substantially and accelerates convolution process. MEC lowers the input matrix in a simple yet efficient/compact way (i.e., much less memory-overhead), and then executes multiple small matrix multiplications in parallel to get convolution completed. Additionally, the reduced memory footprint improves memory sub-system efficiency, improving performance. Our experimental results show that MEC reduces memory consumption significantly with good speedup on both mobile and server platforms, compared with other indirect convolution algorithms. …

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