We offer a short tour into the interactive interpretation of sequential programs. We emphasize streamlike computation — that is, computation of successive bits of information upon request. The core of the approach surveyed here dates back to the work of Berry and the author on sequential algorithms on concrete data structures in the late seventies, culminating in the design of the programming language CDS, in which the semantics of programs of any type can be explored interactively. Around one decade later, two major insights of Cartwright and Felleisen on one hand, and of Lamarche on the other hand gave new, decisive impulses to the study of sequentiality. Cartwright and Felleisen observed that sequential algorithms give a direct semantics to control operators like call-cc and proposed to include explicit errors both in the syntax and in the semantics of the language PCF. Lamarche (unpublished) connected sequential algorithms to linear logic and games. The successful program of games semantics has spanned over the nineties until now, starting with syntax-independent characterizations of the term model of PCF by Abramsky, Jagadeesan, and Malacaria on one hand, and by Hyland and Ong on the other hand.
Sequential algorithms turned out to be quite central in the study of sequentiality. First, let us mention that Kleene has developed (for lower types) similar notions @cite_25 , under the nice name of oracles, in his late works on the semantics of higher order recursion theory (see @cite_17 for a detailed comparison).
@cite_25 @cite_17
2145617779 1547036180
We show that Kleene's theory of unimonotone functions strictly relates to the theory of sequentiality originated by the full abstraction problem for PCF. Unimonotone functions are defined via a class of oracles, which turn out to be alternative descriptions of a subclass of Berry-Curien's sequential algorithms. We study the intrinsic limitations of sequential convex optimization through the lens of feedback information theory. In the oracle model of optimization, an algorithm queries an oracle for noisy information about the unknown objective function and the goal is to (approximately) minimize every function in a given class using as few queries as possible. We show that, in order for a function to be optimized, the algorithm must be able to accumulate enough information about the objective. This, in turn, puts limits on the speed of optimization under specific assumptions on the oracle and the type of feedback. Our techniques are akin to the ones used in statistical literature to obtain minimax lower bounds on the risks of estimation procedures; the notable difference is that, unlike in the case of i.i.d. data, a sequential optimization algorithm can gather observations in a controlled manner, so that the amount of information at each step is allowed to change in time. In particular, we show that optimization algorithms often obey the law of diminishing returns: the signal-to-noise ratio drops as the optimization algorithm approaches the optimum. To underscore the generality of the tools, we use our approach to derive fundamental lower bounds for a certain active learning problem. Overall, the present work connects the intuitive notions of “information” in optimization, experimental design, estimation, and active learning to the quantitative notion of Shannon information. In a document network such as a citation network of scientific documents, web-logs, etc., the content produced by authors exhibits their interest in certain topics. In addition some authors influence other authors' interests. In this work, we propose to model the influence of cited authors along with the interests of citing authors. Moreover, we hypothesize that apart from the citations present in documents, the context surrounding the citation mention provides extra topical information about the cited authors. However, associating terms in the context to the cited authors remains an open problem. We propose novel document generation schemes that incorporate the context while simultaneously modeling the interests of citing authors and influence of the cited authors. Our experiments show significant improvements over baseline models for various evaluation criteria such as link prediction between document and cited author, and quantitatively explaining unseen text. The old Asian legend about the blind men and the elephant comes to mind when looking at how different authors of scientific papers describe a piece of related prior work. It turns out that different citations to the same paper often focus on different aspects of that paper and that neither provides a full description of its full set of contributions. In this article, we will describe our investigation of this phenomenon. We studied citation summaries in the context of research papers in the biomedical domain. A citation summary is the set of citing sentences for a given article and can be used as a surrogate for the actual article in a variety of scenarios. It contains information that was deemed by peers to be important. Our study shows that citation summaries overlap to some extent with the abstracts of the papers and that they also differ from them in that they focus on different aspects of these papers than do the abstracts. In addition to this, co-cited articles (which are pairs of articles cited by another article) tend to be similar. We show results based on a lexical similarity metric called cohesion to justify our claims. © 2008 Wiley Periodicals, Inc. Prediction markets are economic mechanisms for aggregating information about future events through sequential interactions with traders. The pricing mechanisms in these markets are known to be related to optimization algorithms in machine learning and through these connections we have some understanding of how equilibrium market prices relate to the beliefs of the traders in a market. However, little is known about rates and guarantees for the convergence of these sequential mechanisms, and two recent papers cite this as an important open question. In this paper we show how some previously studied prediction market trading models can be understood as a natural generalization of randomized coordinate descent which we call randomized subspace descent (RSD). We establish convergence rates for RSD and leverage them to prove rates for the two prediction market models above, answering the open questions. Our results extend beyond standard centralized markets to arbitrary trade networks. In the semantics of programming, finite data types such as finite lists, have traditionally been modelled by initial algebras. Later final coalgebras were used in order to deal with infinite data types. Coalgebras, which are the dual of algebras, turned out to be suited, moreover, as models for certain types of automata and more generally, for (transition and dynamical) systems. An important property of initial algebras is that they satisfy the familiar principle of induction. Such a principle was missing for coalgebras until the work of Aczel (1988) on a theory of non-wellfounded sets, in which he introduced a proof principle nowadays called coinduction. It was formulated in terms of bisimulation, a notion originally stemming from the world of concurrent programming languages (Milner, 1980; Park, 1981). Using the notion of coalgebra homomorphism, the definition of bisimulation on coalgebras can be shown to be formally dual to that of congruence on algebras (Aczel and Mendler, 1989). Thus the three basic notions of universal algebra: algebra, homomorphism of algebras, and congruence, turn out to correspond to: coalgebra, homomorphism of coalgebras, and bisimulation, respectively. In this paper, the latter are taken as the basic ingredients of a theory called universal coalgebra. Some standard results from universal algebra are reformulated (using the afore mentioned correspondence) and proved for a large class of coalgebras, leading to a series of results on, e.g., the lattices of subcoalgebras and bisimulations, simple coalgebras and coinduction, and a covariety theorem for coalgebras similar to Birkhoff''s variety theorem. Abstract The polynomial-time hierarchy is that subrecursive analog of the Kleene arithmetical hierarchy in which deterministic (nondeterministic) polynomial time plays the role of recursive (recursively enumerable) time. Known properties of the polynomial-time hierarchy are summarized. A word problem which is complete in the second stage of the hierarchy is exhibited. In the analogy between the polynomial-time hierarchy and the arithmetical hierarchy, the first order theory of equality plays the role of elementary arithmetic (as the ω-jump of the hierarchy). The problem of deciding validity in the theory of equality is shown to be complete in polynomial-space, and close upper and lower bounds on the space complexity of this problem are established. Abstract Transfinite semantics is a semantics according to which program executions can continue working after an infinite number of steps. Such a view of programs can be useful in the theory of program transformations. So far, transfinite semantics have been succesfully defined for iterative loops. This paper provides an exhaustive definition for semantics that enable also infinitely deep recursion. The definition is actually a parametric schema that defines a family of different transfinite semantics. As standard semantics also match the same schema, our framework describes both standard and transfinite semantics in a uniform way. All semantics are expressed as greatest fixpoints of monotone operators on some complete lattices. It turns out that, for transfinite semantics, the corresponding lattice operators are cocontinuous. According to Kleene’s theorem, this shows that transfinite semantics can be expressed as a limit of iteration which is not transfinite. In order to define models of simply typed functional programming languages being closer to the operational semantics of these languages, the notions of sequentiality, stability and seriality were introduced. These works originated from the definability problem for PCF, posed in [Sco72], and the full abstraction problem for PCF, raised in [Plo77]. Researchers have demonstrated state-of-the-art performance in sequential decision making problems (e.g., robotics control, sequential prediction) with deep neural network models. One often has access to near-optimal oracles that achieve good performance on the task during training. We demonstrate that AggreVaTeD --- a policy gradient extension of the Imitation Learning (IL) approach of (Ross & Bagnell, 2014) --- can leverage such an oracle to achieve faster and better solutions with less training data than a less-informed Reinforcement Learning (RL) technique. Using both feedforward and recurrent neural network predictors, we present stochastic gradient procedures on a sequential prediction task, dependency-parsing from raw image data, as well as on various high dimensional robotics control problems. We also provide a comprehensive theoretical study of IL that demonstrates we can expect up to exponentially lower sample complexity for learning with AggreVaTeD than with RL algorithms, which backs our empirical findings. Our results and theory indicate that the proposed approach can achieve superior performance with respect to the oracle when the demonstrator is sub-optimal. Recent years have seen growing interest in high-level languages for programming networks. But the design of these languages has been largely ad hoc, driven more by the needs of applications and the capabilities of network hardware than by foundational principles. The lack of a semantic foundation has left language designers with little guidance in determining how to incorporate new features, and programmers without a means to reason precisely about their code. This paper presents NetKAT, a new network programming language that is based on a solid mathematical foundation and comes equipped with a sound and complete equational theory. We describe the design of NetKAT, including primitives for filtering, modifying, and transmitting packets; union and sequential composition operators; and a Kleene star operator that iterates programs. We show that NetKAT is an instance of a canonical and well-studied mathematical structure called a Kleene algebra with tests (KAT) and prove that its equational theory is sound and complete with respect to its denotational semantics. Finally, we present practical applications of the equational theory including syntactic techniques for checking reachability, proving non-interference properties that ensure isolation between programs, and establishing the correctness of compilation algorithms. A citing sentence is one that appears in a scientific article and cites previous work. Citing sentences have been studied and used in many applications. For example, they have been used in scientific paper summarization, automatic survey generation, paraphrase identification, and citation function classification. Citing sentences that cite multiple papers are common in scientific writing. This observation should be taken into consideration when using citing sentences in applications. For instance, when a citing sentence is used in a summary of a scientific paper, only the fragments of the sentence that are relevant to the summarized paper should be included in the summary. In this paper, we present and compare three different approaches for identifying the fragments of a citing sentence that are related to a given target reference. Our methods are: word classification, sequence labeling, and segment classification. Our experiments show that segment classification achieves the best results. From the Publisher: Since the introduction of Hoares' Communicating Sequential Processes notation, powerful new tools have transformed CSP into a practical way of describing industrial-sized problems. This book gives you the fundamental grasp of CSP concepts you'll need to take advantage of those tools.Part I provides a detailed foundation for working with CSP, using as little mathematics as possible. It introduces the ideas behind operational, denotational and algebraic models of CSP. Parts II and III go into greater detail about theory and practice. Topics include: parallel operators, hiding and renaming, piping and enslavement, buffers and communication, termination and sequencing, and semantic theory. Three detailed practical case studies are also presented.For anyone interested in modeling sequential processes. Recently, researchers have demonstrated state-of-the-art performance on sequential prediction problems using deep neural networks and Reinforcement Learning (RL). For some of these problems, oracles that can demonstrate good performance may be available during training, but are not used by plain RL methods. To take advantage of this extra information, we propose AggreVaTeD, an extension of the Imitation Learning (IL) approach of Ross & Bagnell (2014). AggreVaTeD allows us to use expressive differentiable policy representations such as deep networks, while leveraging training-time oracles to achieve faster and more accurate solutions with less training data. Specifically, we present two gradient procedures that can learn neural network policies for several problems, including a sequential prediction task and several high-dimensional robotics control problems. We also provide a comprehensive theoretical study of IL that demonstrates that we can expect up to exponentially-lower sample complexity for learning with AggreVaTeD than with plain RL algorithms. Our results and theory indicate that IL (and AggreVaTeD in particular) can be a more effective strategy for sequential prediction than plain RL. Abstract Documents in computer-readable form can be used to provide information about other documents, i.e. those they cite. To do this efficiently requires procedures for computer recognition of citing statements. This is not easy, especially for multi-sentence citing statements. Computer recognition procedures have been developed which are accurate to the following extent: 73 of the words in statements selected by computer procedures as being citing statements are words which are correctly attributable to the corresponding documents. The retrieval effectiveness of computer-recognized citing statements was tested in the following way. First, for eight retrieval requests in inorganiic chemistry, average recall by search of Chemical Abstracts Service indexing and Chemical Abstracts abstract text words was found to be 50 . Words from citing statements referring to the papers to be retrieved were then added to the index terms and abstract words as additional access points, and searching was repeated. Average recall increased to 70 . Only words from citing statements published within a year of the cited papers were used. The retrieval effect of citing statement words alone (published within a year) without index or abstract terms was the following: average recall was 40 . When just the words of the titles of the cited papers were added to those citing statement words, average recall increased to 50 . In this paper we show that Shannon's general purpose analog computer (GPAC) is equivalent to a particular class of recursive functions over the reals with the flavour of Kleene's classical recursive function theory.We first consider the GPAC and several of its extensions to show that all these models have drawbacks and we introduce an alternative continuous-time model of computation that solves these problems. We also show that this new model preserves all the significant relations involving the previous models (namely, the equivalence with the differentially algebraic functions).We then continue with the topic of recursive functions over the reals, and we show full connections between functions generated by the model introduced so far and a particular class of recursive functions over the reals. A fertile field of research in theoretical computer science investigates the rep- resentation of general recursive functions in intensional type theories. Among the most successful approaches are: the use of wellfounded relations, implementation of operational semantics, formalization of domain theory, and inductive definition of domain predicates. Here, a different solution is proposed: exploiting coinductive types to model infinite com- putations. To every type A we associate a type of partial elements A � , coinductively generated by two constructors: the first, p aq just returns an element a: A; the second, ⊲ x, adds a computation step to a recursive element x: A � . We show how this simple device is sufficient to formalize all recursive functions between two given types. It allows the definition of fixed points of finitary, that is, continuous, operators. We will compare this approach to different ones from the literature. Finally, we mention that the formalization, with appropriate structural maps, defines a strong monad. This paper introduces a model of ‘theory of mind’, namely, how we represent the intentions and goals of others to optimise our mutual interactions. We draw on ideas from optimum control and game theory to provide a ‘game theory of mind’. First, we consider the representations of goals in terms of value functions that are prescribed by utility or rewards. Critically, the joint value functions and ensuing behaviour are optimised recursively, under the assumption that I represent your value function, your representation of mine, your representation of my representation of yours, and so on ad infinitum. However, if we assume that the degree of recursion is bounded, then players need to estimate the opponent's degree of recursion (i.e., sophistication) to respond optimally. This induces a problem of inferring the opponent's sophistication, given behavioural exchanges. We show it is possible to deduce whether players make inferences about each other and quantify their sophistication on the basis of choices in sequential games. This rests on comparing generative models of choices with, and without, inference. Model comparison is demonstrated using simulated and real data from a ‘stag-hunt’. Finally, we note that exactly the same sophisticated behaviour can be achieved by optimising the utility function itself (through prosocial utility), producing unsophisticated but apparently altruistic agents. This may be relevant ethologically in hierarchal game theory and coevolution. In sequential decision-making problems under uncertainty, an agent makes decisions, one after another, considering the current state of the environment where she evolves. In most work, the environment the agent evolves in is assumed to be stationary, i.e., its dynamics do not change over time. However, the stationarity hypothesis can be invalid if, for instance, exogenous events can occur. In this document, we are interested in sequential decision-making in non-stationary environments. We propose a new model named HS3MDP, allowing us to represent non-stationary problems whose dynamics evolve among a finite set of contexts. In order to efficiently solve those problems, we adapt the POMCP algorithm to HS3MDPs. We also present RLCD with SCD, a new method to learn the dynamics of the environments, without knowing a priori the number of contexts. We then explore the field of argumentation problems, where few works consider sequential decision-making. We address two types of problems: stochastic debates (APS ) and mediation problems with non-stationary agents (DMP). In this work, we present a model formalizing APS and allowing us to transform them into an MOMDP in order to optimize the sequence of arguments of one agent in the debate. We then extend this model to DMPs to allow a mediator to strategically organize speak-turns in a debate. In this work, we address the problem of joint modeling of text and citations in the topic modeling framework. We present two different models called the Pairwise-Link-LDA and the Link-PLSA-LDA models. The Pairwise-Link-LDA model combines the ideas of LDA [4] and Mixed Membership Block Stochastic Models [1] and allows modeling arbitrary link structure. However, the model is computationally expensive, since it involves modeling the presence or absence of a citation (link) between every pair of documents. The second model solves this problem by assuming that the link structure is a bipartite graph. As the name indicates, Link-PLSA-LDA model combines the LDA and PLSA models into a single graphical model. Our experiments on a subset of Citeseer data show that both these models are able to predict unseen data better than the baseline model of Erosheva and Lafferty [8], by capturing the notion of topical similarity between the contents of the cited and citing documents. Our experiments on two different data sets on the link prediction task show that the Link-PLSA-LDA model performs the best on the citation prediction task, while also remaining highly scalable. In addition, we also present some interesting visualizations generated by each of the models.