Garima Singh

Just as data sets from next-generation experiments grow, processing requirements for physics analysis become more computationally demanding, necessitating performance optimizations for RooFit. One possibility to speed-up minimization and add stability is the use of Automatic Differentiation (AD). Unlike for numerical differentiation, the computation cost scales linearly with the number of parameters, making AD particularly appealing for statistical models with many parameters. In this paper, we report on one possible way to implement AD in RooFit. Our approach is to add a facility to generate C++ code for a full RooFit model automatically. Unlike the original RooFit model, this generated code is free of virtual function calls and other RooFit-specific overhead. In particular, this code is then used to produce the gradient automatically with Clad. Clad is a source transformation AD tool implemented as a plugin to the clang compiler, which automatically generates the derivative code for input C++ functions. We show results demonstrating the improvements observed when applying this code generation strategy to HistFactory and other commonly used RooFit models. HistFactory is the subcomponent of RooFit that implements binned likelihood models with probability densities based on histogram templates. These models frequently have a very large number of free parameters and are thus an interesting first target for AD support in RooFit.

With the growing datasets of current and next-generation HighEnergy and Nuclear Physics (HEP/NP) experiments, statistical analysis has become more computationally demanding. These increasing demands elicit improvements and modernizations in existing statistical analysis software. One way to address these issues is to improve parameter estimation performance and numeric stability using Automatic Differentiation (AD). AD’s computational efficiency and accuracy are superior to the preexisting numerical differentiation techniques, and it offers significant performance gains when calculating the derivatives of functions with a large number of inputs, making it particularly appealing for statistical models with many parameters. For such models, many HEP/NP experiments use RooFit, a toolkit for statistical modeling and fitting that is part of ROOT.In this paper, we report on the effort to support the AD of RooFit likelihood functions. Our approach is to extend RooFit with a tool that generates overheadfree C++ code for a full likelihood function built from RooFit functional models. Gradients are then generated using Clad, a compiler-based source-codetransformation AD tool, using this C++ code. We present our results from applying AD to the entire minimization pipeline and profile likelihood calculations of several RooFit and HistFactory models at the LHC-experiment scale. We show significant reductions in calculation time and memory usage for the minimization of such likelihood functions. We also elaborate on this approach’s current limitations and explain our plans for the future.

As we reach the limit of Moore's Law, researchers are exploring different paradigms to achieve unprecedented performance. Approximate Computing (AC), which relies on the ability of applications to tolerate some error in the results to trade-off accuracy for performance, has shown significant promise. Despite the success of AC in domains such as Machine Learning, its acceptance in High-Performance Computing (HPC) is limited due to stringent requirements for accuracy. We need tools and techniques to identify regions of code that are amenable to approximations and their impact on the application output quality to guide developers to employ selective approximation. To this end, we propose CHEF-FP, a flexible, scalable, and easy-to-use source-code transformation tool based on Automatic Differentiation (AD) for analyzing approximation errors in HPC applications. CHEF-FP uses Clad, an efficient AD tool built as a plugin to the Clang compiler and based on the LLVM compiler infrastructure, as a backend and utilizes its AD abilities to evaluate approximation errors in C++ code. CHEF-FP works at the source by injecting error estimation code into the generated adjoints. This enables the error-estimation code to undergo compiler optimizations resulting in improved analysis time and reduced memory usage. We also provide theoretical and architectural augmentations to source code transformation-based AD tools to perform FP error analysis. This paper primarily focuses on analyzing errors introduced by mixed-precision AC techniques. We also show the applicability of our tool in estimating other kinds of errors by evaluating our tool on codes that use approximate functions. Moreover, we demonstrate the speedups CHEF-FP achieved during analysis time compared to the existing state-of-the-art tool due to its ability to generate and insert approximation error estimate code directly into the derivative source.

RooFit is a toolkit for statistical modeling and fitting used by most experiments in particle physics. Just as data sets from next-generation experiments grow, processing requirements for physics analysis become more computationally demanding, necessitating performance optimizations for RooFit. One possibility to speed-up minimization and add stability is the use of Automatic Differentiation (AD). Unlike for numerical differentiation, the computation cost scales linearly with the number of parameters, making AD particularly appealing for statistical models with many parameters. In this paper, we report on one possible way to implement AD in RooFit. Our approach is to add a facility to generate C++ code for a full RooFit model automatically. Unlike the original RooFit model, this generated code is free of virtual function calls and other RooFit-specific overhead. In particular, this code is then used to produce the gradient automatically with Clad. Clad is a source transformation AD tool implemented as a plugin to the clang compiler, which automatically generates the derivative code for input C++ functions. We show results demonstrating the improvements observed when applying this code generation strategy to HistFactory and other commonly used RooFit models. HistFactory is the subcomponent of RooFit that implements binned likelihood models with probability densities based on histogram templates. These models frequently have a very large number of free parameters and are thus an interesting first target for AD support in RooFit.