/pdf/scalable-molecular-dynamics-with-namd-3j7xyc70g4.pdf

Scalable Molecular Dynamics with NAMD

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

The mapping of large-scale human movements is important for urban planning, traffic forecasting and epidemic prevention. Work in animals had suggested that their foraging might be explained in terms of a random walk, a mathematical rendition of a series of random steps, or a Levy flight, a random walk punctuated by occasional larger steps. The role of Levy statistics in animal behaviour is much debated — as explained in an accompanying News Feature — but the idea of extending it to human behaviour was boosted by a report in 2006 of Levy flight-like patterns in human movement tracked via dollar bills. A new human study, based on tracking the trajectory of 100,000 cell-phone users for six months, reveals behaviour close to a Levy pattern, but deviating from it as individual trajectories show a high degree of temporal and spatial regularity: work and other commitments mean we are not as free to roam as a foraging animal. But by correcting the data to accommodate individual variation, simple and predictable patterns in human travel begin to emerge. The cover photo (by Cesar Hidalgo) captures human mobility in New York's Grand Central Station. This study used a sample of 100,000 mobile phone users whose trajectory was tracked for six months to study human mobility patterns. Displacements across all users suggest behaviour close to the Levy-flight-like pattern observed previously based on the motion of marked dollar bills, but with a cutoff in the distribution. The origin of the Levy patterns observed in the aggregate data appears to be population heterogeneity and not Levy patterns at the level of the individual. Despite their importance for urban planning1, traffic forecasting2 and the spread of biological3,4,5 and mobile viruses6, our understanding of the basic laws governing human motion remains limited owing to the lack of tools to monitor the time-resolved location of individuals. Here we study the trajectory of 100,000 anonymized mobile phone users whose position is tracked for a six-month period. We find that, in contrast with the random trajectories predicted by the prevailing Levy flight and random walk models7, human trajectories show a high degree of temporal and spatial regularity, each individual being characterized by a time-independent characteristic travel distance and a significant probability to return to a few highly frequented locations. After correcting for differences in travel distances and the inherent anisotropy of each trajectory, the individual travel patterns collapse into a single spatial probability distribution, indicating that, despite the diversity of their travel history, humans follow simple reproducible patterns. This inherent similarity in travel patterns could impact all phenomena driven by human mobility, from epidemic prevention to emergency response, urban planning and agent-based modelling.

/pdf/understanding-individual-human-mobility-patterns-3k1tyob274.pdf

Understanding individual human mobility patterns

“Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial Networks”の学習報告

We study routing problems in time-dependent and edge and/or vertex-labeled transportation networks. Labels allow one to express a number of discrete properties of the edges and nodes. The main focus is a unified algorithm that efficiently solves a number of seemingly unrelated problems in transportation science. Experimental data gained from modeling practical situations suggest that the formalism allows interesting compromises between the conflicting goals of generality and efficiency. 1. We use edge/vertex labels in the framework of Formal Language Constrained Path Problems to handle discrete choice constraints. The label set is usually small and does not depend on the graph. Edge labels induct! path labels, which allows us to impose feasibility constraints on the set of paths considered as shortest path candidates. Second, we propose monotonic piecewise-linear traversal functions to represent the time-dependent aspect of link delays. The applications that can be modeled include scheduled transit and time-windows. 3. Third, we combine the above models and capture a variety of natural problems in transportatiou science such as time-window constrained trip-chaining. The results demonstrate the robustness of the proposed formalisms. As evidence for our claims of practical efficiency in a realistic setting, we report preliminary computational experience from TRANSIMS case studiesmore » of Portland, Oregon.« less

/pdf/routing-in-time-dependent-and-labeled-networks-2gntajmw4a.pdf

Routing in time-dependent and labeled networks

Many researchers have studied symmetry properties of various Boolean
functions. A class of Boolean functions, called nested canalyzing functions
(NCFs), has been used to model certain biological phenomena. We identify some
interesting relationships between NCFs, symmetric Boolean functions and a
generalization of symmetric Boolean functions, which we call $r$-symmetric
functions (where $r$ is the symmetry level). Using a normalized representation
for NCFs, we develop a characterization of when two variables of an NCF are
symmetric. Using this characterization, we show that the symmetry level of an
NCF $f$ can be easily computed given a standard representation of $f$. We also
present an algorithm for testing whether a given $r$-symmetric function is an
NCF. Further, we show that for any NCF $f$ with $n$ variables, the notion of
strong asymmetry considered in the literature is equivalent to the property
that $f$ is $n$-symmetric. We use this result to derive a closed form
expression for the number of $n$-variable Boolean functions that are NCFs and
strongly asymmetric. We also identify all the Boolean functions that are NCFs
and symmetric.

Symmetry Properties of Nested Canalyzing Functions

Several practical instances of network design problems require the network to satisfy multiple constraints. In this paper, we address the Budget Constrained Connected Median Problem: We are given an undirected graph G = (V, E) with two different edge-weight functions c (modeling the construction or communication cost) and d (modeling the service distance), and a bound B on the total service distance. The goal is to find a subtree T of G with minimum c-cost c(T) subject to the constraint that the sum of the service distances of all the remaining nodes υ ∈ V \ T to their closest neighbor in T does not exceed the specified budget B. This problem has applications in optical network design and the efficient maintenance of distributed databases.

We formulate this problem as bicriteria network design problem, and present bicriteria approximation algorithms. We also prove lower bounds on the approximability of the problem that demonstrate that our performance ratios are close to best possible.

/pdf/budget-constrained-minimum-cost-connected-medians-1yaagr847m.pdf

Budget Constrained Minimum Cost Connected Medians

Deep learning classifiers are assisting humans in making decisions and hence the user's trust in these models is of paramount importance. Trust is often a function of constant behavior. From an AI model perspective it means given the same input the user would expect the same output, especially for correct outputs, or in other words consistently correct outputs. This paper studies a model behavior in the context of periodic retraining of deployed models where the outputs from successive generations of the models might not agree on the correct labels assigned to the same input. We formally define consistency and correct-consistency of a learning model. We prove that consistency and correct-consistency of an ensemble learner is not less than the average consistency and correct-consistency of individual learners and correct-consistency can be improved with a probability by combining learners with accuracy not less than the average accuracy of ensemble component learners. To validate the theory using three datasets and two state-of-the-art deep learning classifiers we also propose an efficient dynamic snapshot ensemble method and demonstrate its value.

Wisdom of the Ensemble: Improving Consistency of Deep Learning Models

We prove the #P-hardness of the counting problems associated with various satisfiability, graph and combinatorial problems, when restricted to planar instances. These problems include \begin{romannum} \item[{}] {\sc 3Sat, 1-3Sat, 1-Ex3Sat, Minimum Vertex Cover, Minimum Dominating Set, Minimum Feedback Vertex Set, X3C, Partition Into Triangles, and Clique Cover.} \end{romannum} We also prove the {\sf NP}-completeness of the {\sc Ambiguous Satisfiability} problems \cite{Sa80} and the {\sf D$^P$}-completeness (with respect to random polynomial reducibility) of the unique satisfiability problems \cite{VV85} associated with several of the above problems, when restricted to planar instances. Previously, very few {\sf #P}-hardness results, no {\sf NP}-hardness results, and no {\sf D$^P$}-completeness results were known for counting problems, ambiguous satisfiability problems and unique satisfiability problems, respectively, when restricted to planar instances. 
Assuming {\sf P $\neq $ NP}, one corollary of the above results is 
There are no $\epsilon$-approximation algorithms for the problems of maximizing or minimizing a linear objective function subject to a planar system of linear inequality constraints over the integers.

Madhav V. Marathe

Papers

Routing in time-dependent and labeled networks

Symmetry Properties of Nested Canalyzing Functions

Budget Constrained Minimum Cost Connected Medians

Wisdom of the Ensemble: Improving Consistency of Deep Learning Models

The Complexity of Planar Counting Problems