Computing Petaflops over Terabytes of Data: The Case of Genome-Wide Association Studies

In many scientific and engineering applications, one has to solve not one but a sequence of instances of the same problem. Often times, the problems in the sequence are linked in a way that allows intermediate results to be reused. A characteristic example for this class of applications is given by the Genome-Wide Association Studies (GWAS), a widely spread tool in computational biology. GWAS entails the solution of up to trillions ($10^{12}$) of correlated generalized least-squares problems, posing a daunting challenge: the performance of petaflops ($10^{15}$ floating-point operations) over terabytes of data. In this paper, we design an algorithm for performing GWAS on multi-core architectures. This is accomplished in three steps. First, we show how to exploit the relation among successive problems, thus reducing the overall computational complexity. Then, through an analysis of the required data transfers, we identify how to eliminate any overhead due to input/output operations. Finally, we study how to decompose computation into tasks to be distributed among the available cores, to attain high performance and scalability. With our algorithm, a GWAS that currently requires the use of a supercomputer may now be performed in matter of hours on a single multi-core node. The discussion centers around the methodology to develop the algorithm rather than the specific application. We believe the paper contributes valuable guidelines of general applicability for computational scientists on how to develop and optimize numerical algorithms

Exploiting Natural On-chip Redundancy for Energy Efficient Memory and Computing

Power density is currently the primary design constraint across most computing segments and the main performance limiting factor. For years, industry has kept power density constant, while increasing frequency, lowering transistors supply (Vdd) and threshold (Vth) voltages. However, Vth scaling has stopped because leakage current is exponentially related to it. Transistor count and integration density keep doubling every process generation (Moore’s Law), but the power budget caps the amount of hardware that can be active at the same time, leading to dark silicon. With each new generation, there are more resources available, but we cannot fully exploit their performance potential. In the last years, different research trends have explored how to cope with dark silicon and unlock the energy efficiency of the chips, including Near-Threshold voltage Computing (NTC) and approximate computing. NTC aggressively lowers Vdd to values near Vth. This allows a substantial reduction in power, as dynamic power scales quadratically with supply voltage. The resultant power reduction could be used to activate more chip resources and potentially achieve performance improvements. Unfortunately, Vdd scaling is limited by the tight functionality margins of on-chip SRAM transistors. When scaling Vdd down to values near-threshold, manufacture-induced parameter variations affect the functionality of SRAM cells, which eventually become not reliable. A large amount of emerging applications, on the other hand, features an intrinsic error-resilience property, tolerating a certain amount of noise. In this context, approximate computing takes advantage of this observation and exploits the gap between the level of accuracy required by the application and the level of accuracy given by the computation, providing that reducing the accuracy translates into an energy gain. However, deciding which instructions and data and which techniques are best suited for approximation still poses a major challenge. This dissertation contributes in these two directions. First, it proposes a new approach to mitigate the impact of SRAM failures due to parameter variation for effective operation at ultra-low voltages. We identify two levels of natural on-chip redundancy: cache level and content level. The first arises because of the replication of blocks in multi-level cache hierarchies. We exploit this redundancy with a cache management policy that allocates blocks to entries taking into account the nature of the cache entry and the use pattern of the block. This policy obtains performance improvements between 2% and 34%, with respect to block disabling, a technique with similar complexity, incurring no additional storage overhead. The latter (content level redundancy) arises because of the redundancy of data in real world applications. We exploit this redundancy compressing cache blocks to fit them in partially functional cache entries. At the cost of a slight overhead increase, we can obtain performance within 2% of that obtained when the cache is built with fault-free cells, even if more than 90% of the cache entries have at least a faulty cell. Then, we analyze how the intrinsic noise tolerance of emerging applications can be exploited to design an approximate Instruction Set Architecture (ISA). Exploiting the ISA redundancy, we explore a set of techniques to approximate the execution of instructions across a set of emerging applications, pointing out the potential of reducing the complexity of the ISA, and the trade-offs of the approach. In a proof-of-concept implementation, the ISA is shrunk in two dimensions: Breadth (i.e., simplifying instructions) and Depth (i.e., dropping instructions). This proof-of-concept shows that energy can be reduced on average 20.6% at around 14.9% accuracy loss

Database Learning: Toward a Database that Becomes Smarter Every Time

In today's databases, previous query answers rarely benefit answering future queries. For the first time, to the best of our knowledge, we change this paradigm in an approximate query processing (AQP) context. We make the following observation: the answer to each query reveals some degree of knowledge about the answer to another query because their answers stem from the same underlying distribution that has produced the entire dataset. Exploiting and refining this knowledge should allow us to answer queries more analytically, rather than by reading enormous amounts of raw data. Also, processing more queries should continuously enhance our knowledge of the underlying distribution, and hence lead to increasingly faster response times for future queries. We call this novel idea---learning from past query answers---Database Learning. We exploit the principle of maximum entropy to produce answers, which are in expectation guaranteed to be more accurate than existing sample-based approximations. Empowered by this idea, we build a query engine on top of Spark SQL, called Verdict. We conduct extensive experiments on real-world query traces from a large customer of a major database vendor. Our results demonstrate that Verdict supports 73.7% of these queries, speeding them up by up to 23.0x for the same accuracy level compared to existing AQP systems.Comment: This manuscript is an extended report of the work published in ACM SIGMOD conference 201

Research and Education in Computational Science and Engineering

Over the past two decades the field of computational science and engineering (CSE) has penetrated both basic and applied research in academia, industry, and laboratories to advance discovery, optimize systems, support decision-makers, and educate the scientific and engineering workforce. Informed by centuries of theory and experiment, CSE performs computational experiments to answer questions that neither theory nor experiment alone is equipped to answer. CSE provides scientists and engineers of all persuasions with algorithmic inventions and software systems that transcend disciplines and scales. Carried on a wave of digital technology, CSE brings the power of parallelism to bear on troves of data. Mathematics-based advanced computing has become a prevalent means of discovery and innovation in essentially all areas of science, engineering, technology, and society; and the CSE community is at the core of this transformation. However, a combination of disruptive developments---including the architectural complexity of extreme-scale computing, the data revolution that engulfs the planet, and the specialization required to follow the applications to new frontiers---is redefining the scope and reach of the CSE endeavor. This report describes the rapid expansion of CSE and the challenges to sustaining its bold advances. The report also presents strategies and directions for CSE research and education for the next decade.Comment: Major revision, to appear in SIAM Revie

Exploiting the Statistics of Learning and Inference

When dealing with datasets containing a billion instances or with simulations that require a supercomputer to execute, computational resources become part of the equation. We can improve the efficiency of learning and inference by exploiting their inherent statistical nature. We propose algorithms that exploit the redundancy of data relative to a model by subsampling data-cases for every update and reasoning about the uncertainty created in this process. In the context of learning we propose to test for the probability that a stochastically estimated gradient points more than 180 degrees in the wrong direction. In the context of MCMC sampling we use stochastic gradients to improve the efficiency of MCMC updates, and hypothesis tests based on adaptive mini-batches to decide whether to accept or reject a proposed parameter update. Finally, we argue that in the context of likelihood free MCMC one needs to store all the information revealed by all simulations, for instance in a Gaussian process. We conclude that Bayesian methods will remain to play a crucial role in the era of big data and big simulations, but only if we overcome a number of computational challenges.Comment: Proceedings of the NIPS workshop on "Probabilistic Models for Big Data