Sequential Gaussian Processes for Online Learning of Nonstationary Functions

Many machine learning problems can be framed in the context of estimating functions, and often these are time-dependent functions that are estimated in real-time as observations arrive. Gaussian processes (GPs) are an attractive choice for modeling real-valued nonlinear functions due to their flexibility and uncertainty quantification. However, the typical GP regression model suffers from several drawbacks: i) Conventional GP inference scales $O(N^{3})$ with respect to the number of observations; ii) updating a GP model sequentially is not trivial; and iii) covariance kernels often enforce stationarity constraints on the function, while GPs with non-stationary covariance kernels are often intractable to use in practice. To overcome these issues, we propose an online sequential Monte Carlo algorithm to fit mixtures of GPs that capture non-stationary behavior while allowing for fast, distributed inference. By formulating hyperparameter optimization as a multi-armed bandit problem, we accelerate mixing for real time inference. Our approach empirically improves performance over state-of-the-art methods for online GP estimation in the context of prediction for simulated non-stationary data and hospital time series data

Transformations of High-Level Synthesis Codes for High-Performance Computing

Specialized hardware architectures promise a major step in performance and energy efficiency over the traditional load/store devices currently employed in large scale computing systems. The adoption of high-level synthesis (HLS) from languages such as C/C++ and OpenCL has greatly increased programmer productivity when designing for such platforms. While this has enabled a wider audience to target specialized hardware, the optimization principles known from traditional software design are no longer sufficient to implement high-performance codes. Fast and efficient codes for reconfigurable platforms are thus still challenging to design. To alleviate this, we present a set of optimizing transformations for HLS, targeting scalable and efficient architectures for high-performance computing (HPC) applications. Our work provides a toolbox for developers, where we systematically identify classes of transformations, the characteristics of their effect on the HLS code and the resulting hardware (e.g., increases data reuse or resource consumption), and the objectives that each transformation can target (e.g., resolve interface contention, or increase parallelism). We show how these can be used to efficiently exploit pipelining, on-chip distributed fast memory, and on-chip streaming dataflow, allowing for massively parallel architectures. To quantify the effect of our transformations, we use them to optimize a set of throughput-oriented FPGA kernels, demonstrating that our enhancements are sufficient to scale up parallelism within the hardware constraints. With the transformations covered, we hope to establish a common framework for performance engineers, compiler developers, and hardware developers, to tap into the performance potential offered by specialized hardware architectures using HLS

Efficient Bayesian-based Multi-View Deconvolution

Light sheet fluorescence microscopy is able to image large specimen with high resolution by imaging the sam- ples from multiple angles. Multi-view deconvolution can significantly improve the resolution and contrast of the images, but its application has been limited due to the large size of the datasets. Here we present a Bayesian- based derivation of multi-view deconvolution that drastically improves the convergence time and provide a fast implementation utilizing graphics hardware.Comment: 48 pages, 20 figures, 1 table, under review at Nature Method

Replication or exploration? Sequential design for stochastic simulation experiments

We investigate the merits of replication, and provide methods for optimal design (including replicates), with the goal of obtaining globally accurate emulation of noisy computer simulation experiments. We first show that replication can be beneficial from both design and computational perspectives, in the context of Gaussian process surrogate modeling. We then develop a lookahead based sequential design scheme that can determine if a new run should be at an existing input location (i.e., replicate) or at a new one (explore). When paired with a newly developed heteroskedastic Gaussian process model, our dynamic design scheme facilitates learning of signal and noise relationships which can vary throughout the input space. We show that it does so efficiently, on both computational and statistical grounds. In addition to illustrative synthetic examples, we demonstrate performance on two challenging real-data simulation experiments, from inventory management and epidemiology.Comment: 34 pages, 9 figure