Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Many practical computing problems concern large graphs. Standard examples include the Web graph and various social networks. The scale of these graphs - in some cases billions of vertices, trillions of edges - poses challenges to their efficient processing. In this paper we present a computational model suitable for this task. Programs are expressed as a sequence of iterations, in each of which a vertex can receive messages sent in the previous iteration, send messages to other vertices, and modify its own state and that of its outgoing edges or mutate graph topology. This vertex-centric approach is flexible enough to express a broad set of algorithms. The model has been designed for efficient, scalable and fault-tolerant implementation on clusters of thousands of commodity computers, and its implied synchronicity makes reasoning about programs easier. Distribution-related details are hidden behind an abstract API. The result is a framework for processing large graphs that is expressive and easy to program.

/pdf/pregel-a-system-for-large-scale-graph-processing-30lgjenxxg.pdf

Pregel: a system for large-scale graph processing

where A represents the magnetic vector potential, is an integral of the hydromagnetic equations. This -integral made it possible to formulate a variational principle for the force-free magnetic fields. The integral expresses the fact that motions cannot transform a given field in an entirely arbitrary different field, if the conductivity of the medium isconsidered infinite. In this paper we shall show that the full set of hydromagnetic equations admit five more integrals, besides the energy integral, if dissipative processes are absent. These integrals, as we shall presently verify, are I2 =fbHvdV, (2)

Proceedings of the National Academy of Sciences

Computational geometry

An O(n2.75) algorithm for online topological ordering

A priority queue is a data structure that stores a set of items, each one consisting of a tuple which contains some (satellite) information plus a priority value (also called key) drawn from a totally ordered universe. A priority queue supports the following operations on the processed set: access_minimum (returns the item in the set having minimum key), delete_min (returns and deletes the item in the set having the minimum key) and insert (inserts a new item into the set). Priority queues (hereafter PQs) have numerous important applications: combinatorial optimization (e.g. Dijkstra’s shortest path algorithm [7]), time forward processing [5], job scheduling, event simulation and online sorting, just to cite a few. Many PQ implementations currently exist for small data sets fitting into the internal memory of the computer, e.g. k—ary heaps [23], Fibonacci heaps [10], radix heaps [1], and some of them are also publicly available to the programmers (see e.g. the LEDA library [15]). However, in large-scale event simulations or on instances of very large graph problems (as they recently occur in e.g. geographical information systems), the performance of these internal-memory PQs may significantly deteriorate, thus being a bottleneck for the overall application. In fact, as soon as parts of the PQs do not fit entirely into the internal memory of the computer, but reside in its external memory (e.g. in the hard disk), we may observe a heavy paging activity of the external-memory devices because the pattern of memory accesses is not tuned to exhibit any locality of reference. Due to the technological features of current disk systems [17], this situation may determine a slow down of 5 or 6 orders of magnitude in the final performance of each PQ-operation 1. Consequently, it is required to design PQs which take explicitly into account the physical properties of the disk systems in order to achieve efficient I/O-performances that allow these data structures to be plugged successfully in software libraries.

An Experimental Study of Priority Queues in External Memory

Big Data is no fad. The world is growing at an exponential rate, and so is the size of data collected across the globe. The data is becoming more meaningful and contextually relevant, breaks new ground for machine learning and artificial intelligence (AI), and even moves them from research labs to production. That is, the problem has shifted from collecting massive amounts of data to understanding it, i.e., turning data into knowledge, conclusions, and actions. This Big AI, however, often faces poor scale-up behaviour from algorithms that have been designed based on models of computation that are no longer realistic for Big Data. This special issue constitutes an attempt to highlight the algorithmic challenges and opportunities but also the social and ethical issues of Big Data. Of specific interest and focus have been computation- and resource-efficient algorithms when searching through data to find and mine relevant or pertinent information.

/pdf/from-big-data-to-big-artificial-intelligence-49zti34ogq.pdf

From Big Data to Big Artificial Intelligence

Multisplit is a broadly useful parallel primitive that permutes its input data into contiguous buckets or bins, where the function that categorizes an element into a bucket is provided by the programmer. Due to the lack of an efficient multisplit on GPUs, programmers often choose to implement multisplit with a sort. However, sort does more work than necessary to implement multisplit, and is thus inefficient. In this work, we provide a parallel model and multiple implementations for the multisplit problem. Our principal focus is multisplit for a small number of buckets. In our implementations, we exploit the computational hierarchy of the GPU to perform most of the work locally, with minimal usage of global operations. We also use warp-synchronous programming models to avoid branch divergence and reduce memory usage, as well as hierarchical reordering of input elements to achieve better coalescing of global memory accesses. On an NVIDIA K40c GPU, for key-only (key-value) multisplit, we demonstrate a 3.0-6.7x (4.4-8.0x) speedup over radix sort, and achieve a peak throughput of 10.0 G keys/s.

GPU multisplit

We show how to compute single-source shortest paths in undirected graphs with non-negative edge lengths in O(√nm/Blogn+MST(n,m)I/Os, where n is the number of vertices, m is the number of edges, B is the disk block size, and MST(n,m) is the I/O-cost of computing a minimum spanning tree. For sparse graphs, the new algorithm performs O((n/√B)logn) I/Os. This result removes our previous algorithm's dependence on the edge lengths in the graph.

Ulrich Meyer

Papers

An O(n2.75) algorithm for online topological ordering

An Experimental Study of Priority Queues in External Memory

From Big Data to Big Artificial Intelligence

GPU multisplit

I/O-efficient undirected shortest paths with unbounded edge lengths