We propose a new approach to value function approximation which combines linear temporal difference reinforcement learning with subspace identification. In practical applications, reinforcement learning (RL) is complicated by the fact that state is either high-dimensional or partially observable. Therefore, RL methods are designed to work with features of state rather than state itself, and the success or failure of learning is often determined by the suitability of the selected features. By comparison, subspace identification (SSID) methods are designed to select a feature set which preserves as much information as possible about state. In this paper we connect the two approaches, looking at the problem of reinforcement learning with a large set of features, each of which may only be marginally useful for value function approximation. We introduce a new algorithm for this situation, called Predictive State Temporal Difference (PSTD) learning. As in SSID for predictive state representations, PSTD finds a linear compression operator that projects a large set of features down to a small set that preserves the maximum amount of predictive information. As in RL, PSTD then uses a Bellman recursion to estimate a value function. We discuss the connection between PSTD and prior approaches in RL and SSID. We prove that PSTD is statistically consistent, perform several experiments that illustrate its properties, and demonstrate its potential on a difficult optimal stopping problem.
Second, we look at the problem of value function estimation from a model-based perspective (). Instead of learning a linear transition model from features, as in @cite_33 , we use subspace identification @cite_20 @cite_27 to learn a PSR from our samples. Then we compute a value function via the Bellman equations for our learned PSR @. This new approach has a substantial benefit: while the linear feature-to-feature transition model of @cite_33 does not seem to have any common uses outside that paper, PSRs have been proposed numerous times on their own merits (including being invented independently at least three times), and are a strict generalization of POMDPs.
@cite_27 @cite_33 @cite_20
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Over the past decade there has been considerable interest in spectral algorithms for learning Predictive State Representations (PSRs). Spectral algorithms have appealing theoretical guarantees; however, the resulting models do not always perform well on inference tasks in practice. One reason for this behavior is the mismatch between the intended task (accurate filtering or prediction) and the loss function being optimized by the algorithm (estimation error in model parameters). A natural idea is to improve performance by refining PSRs using an algorithm such as EM. Unfortunately it is not obvious how to apply apply an EM style algorithm in the context of PSRs as the Log Likelihood is not well defined for all PSRs. We show that it is possible to overcome this problem using ideas from Predictive State Inference Machines. We combine spectral algorithms for PSRs as a consistent and efficient initialization with PSIM-style updates to refine the resulting model parameters. By combining these two ideas we develop Inference Gradients, a simple, fast, and robust method for practical learning of PSRs. Inference Gradients performs gradient descent in the PSR parameter space to optimize an inference-based loss function like PSIM. Because Inference Gradients uses a spectral initialization we get the same consistency benefits as PSRs. We show that Inference Gradients outperforms both PSRs and PSIMs on real and synthetic data sets. Predictive State Representations (PSRs) are an expressive class of models for controlled stochastic processes. PSRs represent state as a set of predictions of future observable events. Because PSRs are defined entirely in terms of observable data, statistically consistent estimates of PSR parameters can be learned efficiently by manipulating moments of observed training data. Most learning algorithms for PSRs have assumed that actions and observations are finite with low cardinality. In this paper, we generalize PSRs to infinite sets of observations and actions, using the recent concept of Hilbert space embeddings of distributions. The essence is to represent the state as a nonparametric conditional embedding operator in a Reproducing Kernel Hilbert Space (RKHS) and leverage recent work in kernel methods to estimate, predict, and update the representation. We show that these Hilbert space embeddings of PSRs are able to gracefully handle continuous actions and observations, and that our learned models outperform competing system identification algorithms on several prediction benchmarks. 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. Predictive state representations (PSRs) offer an expressive framework for modelling partially observable systems. By compactly representing systems as functions of observable quantities, the PSR learning approach avoids using local-minima prone expectation-maximization and instead employs a globally optimal moment-based algorithm. Moreover, since PSRs do not require a predetermined latent state structure as an input, they offer an attractive framework for model-based reinforcement learning when agents must plan without a priori access to a system model. Unfortunately, the expressiveness of PSRs comes with significant computational cost, and this cost is a major factor inhibiting the use of PSRs in applications. In order to alleviate this shortcoming, we introduce the notion of compressed PSRs (CPSRs). The CPSR learning approach combines recent advancements in dimensionality reduction, incremental matrix decomposition, and compressed sensing. We show how this approach provides a principled avenue for learning accurate approximations of PSRs, drastically reducing the computational costs associated with learning while also providing effective regularization. Going further, we propose a planning framework which exploits these learned models. And we show that this approach facilitates model-learning and planning in large complex partially observable domains, a task that is infeasible without the principled use of compression. Modeling dynamical systems, both for control purposes and to make predictions about their behavior, is ubiquitous in science and engineering. Predictive state representations (PSRs) are a recently introduced class of models for discrete-time dynamical systems. The key idea behind PSRs and the closely related OOMs (Jaeger's observable operator models) is to represent the state of the system as a set of predictions of observable outcomes of experiments one can do in the system. This makes PSRs rather different from history-based models such as nth-order Markov models and hidden-state-based models such as HMMs and POMDPs. We introduce an interesting construct, the system-dynamics matrix, and show how PSRs can be derived simply from it. We also use this construct to show formally that PSRs are more general than both nth-order Markov models and HMMs POMDPs. Finally, we discuss the main difference between PSRs and OOMs and conclude with directions for future work. Predictive state representations (PSRs) are a recently proposed way of modeling controlled dynamical systems. PSR-based models use predictions of observable outcomes of tests that could be done on the system as their state representation, and have model parameters that define how the predictive state representation changes over time as actions are taken and observations noted. Learning PSR-based models requires solving two subproblems: 1) discovery of the tests whose predictions constitute state, and 2) learning the model parameters that define the dynamics. So far, there have been no results available on the discovery subproblem while for the learning subproblem an approximate-gradient algorithm has been proposed (, 2003) with mixed results (it works on some domains and not on others). In this paper, we provide the first discovery algorithm and a new learning algorithm for linear PSRs for the special class of controlled dynamical systems that have a reset operation. We provide experimental verification of our algorithms. Finally, we also distinguish our work from prior work by Jaeger (2000) on observable operator models (OOMs). Predictive state representations (PSRs) have recently been proposed as an alternative to partially observable Markov decision processes (POMDPs) for representing the state of a dynamical system (, 2001). We present a learning algorithm that learns a PSR from observational data. Our algorithm produces a variant of PSRs called transformed predictive state representations (TPSRs). We provide an efficient principal-components-based algorithm for learning a TPSR, and show that TPSRs can perform well in comparison to Hidden Markov Models learned with Baum-Welch in a real world robot tracking task for low dimensional representations and long prediction horizons. Historically, papers have been physically bound to the journal in which they were published; but in the digital age papers are available individually, no longer tied to their respective journals. Hence, papers now can be read and cited based on their own merits, independently of the journal's physical availability, reputation, or impact factor (IF). We compare the strength of the relationship between journals' IFs and the actual citations received by their respective papers from 1902 to 2009. Throughout most of the 20th century, papers' citation rates were increasingly linked to their respective journals' IFs. However, since 1990, the advent of the digital age, the relation between IFs and paper citations has been weakening. This began first in physics, a field that was quick to make the transition into the electronic domain. Furthermore, since 1990 the overall proportion of highly cited papers coming from highly cited journals has been decreasing and, of these highly cited papers, the proportion not coming from highly cited journals has been increasing. Should this pattern continue, it might bring an end to the use of the IF as a way to evaluate the quality of journals, papers, and researchers. © 2012 Wiley Periodicals, Inc. It has recently been proposed that it is advantageous to have models of dynamical systems be based solely on observable quantities. Predictive state representations (PSRs) are a type of model that uses predictions about future observations to capture the state of a dynamical system. However, PSRs do not use memory of past observations. We propose a model called memory-PSRs that uses both memories of the past, and predictions of the future. We show that the use of memories provides a number of potential advantages. It can reduce the size of the model (in comparison to a PSR model). In addition many dynamical systems have memories that can serve as landmarks that completely determine the current state. The detection and recognition of landmarks is advantageous because they can serve to reset a model that has gotten off-track, as often happens when the model is learned from samples. This paper develops both memory-PSRs and the use and detection of landmarks. Purpose – The purpose of this paper is to suggest an alternative to the widely used Times Cited criterion for analysing citation networks. The approach involves taking account of the natures of the papers that cite a given paper, so as to differentiate between papers that attract the same number of citations.Design methodology approach – ArticleRank is an algorithm that has been derived from Google's PageRank algorithm to measure the influence of journal articles. ArticleRank is applied to two datasets – a citation network based on an early paper on webometrics, and a self‐citation network based on the 19 most cited papers in the Journal of Documentation – using citation data taken from the Web of Knowledge database.Findings – ArticleRank values provide a different ranking of a set of papers from that provided by the corresponding Times Cited values, and overcomes the inability of the latter to differentiate between papers with the same numbers of citations. The difference in rankings between Times Cited ... Predictive state representations (PSRs) model dynamical systems using appropriately chosen predictions about future observations as a representation of the current state. In contrast to the hidden states posited by HMMs or RNNs, PSR states are directly observable in the training data; this gives rise to a moment-matching spectral algorithm for learning PSRs that is computationally efficient and statistically consistent when the model complexity matches that of the true system generating the data. In practice, however, model mismatch is inevitable and while spectral learning remains appealingly fast and simple it may fail to find optimal models. To address this problem, we investigate the use of gradient methods for improving spectrally-learned PSRs. We show that only a small amount of additional gradient optimization can lead to significant performance gains, and moreover that initializing gradient methods with the spectral learning solution yields better models in significantly less time than starting from scratch. Partial Spectrum Reuse (PSR) in the second tier of two-tier heterogeneous cellular networks has a potential to improve spectrum efficiency by reducing inter-cell interference, and thus energy efficiency as well by deploying less or switching off more Base Stations (BSs). In this paper, we analyze the optimal PSR factor, defined as the portion of spectrum reused by micro cells in two-tier heterogeneous networks, which is not in an explicit form generally. Then, a closed-form limit of the optimal PSR factor is derived as the ratio of the user rate requirement over the whole system spectrum bandwidth is approaching zero, based on which a threshold of the micro-BS energy cost is also derived to determine which type of BSs is preferable. Specifically, one should deploy more micro BSs or switch off more macro BSs if the micro-BS energy cost is lower than the threshold. Otherwise, the optimal choice is the opposite. This threshold with the PSR scheme is higher than that without PSR scheme, i.e., PSR can improve both spectrum efficiency and energy efficiency. Numerical results show that adopting PSR can reduce the network energy consumption by up to 50 when the transmit power of macro BSs is 10dB higher than that of micro BSs. We investigate the minimization of Newton's functional for the problem of the body of minimal resistance with maximal height @math cite butt in the class of convex developable functions defined in a disc. This class is a natural candidate to find a (non-radial) minimizer in accordance with the results of cite lrp2. We prove that the minimizer in this class has a minimal set in the form of a regular polygon with @math sides centered in the disc, and numerical experiments indicate that the natural number @math is a non-decreasing function of @math . The corresponding functions all achieve a lower value of the functional than the optimal radially symmetric function with the same height @math . Knowledge Tracing (BKT) is a common way of determining student knowledge of skills in adaptive educational systems and cognitive tutors. The basic BKT is a Hidden Markov Model (HMM) that models student knowledge based on five parameters: prior, learn rate, forget, guess, and slip. Expectation Maximization (EM) is often used to learn these parameters from training data. However, EM is a time-consuming process, and is prone to converging to erroneous, implausible local optima depending on the initial values of the BKT parameters. In this paper we address these two problems by using spectral learning to learn a Predictive State Representation (PSR) that represents the BKT HMM. We then use a heuristic to extract the BKT parameters from the learned PSR using basic matrix operations. The spectral learning method is based on an approximate factorization of the estimated covariance of windows from students' sequences of correct and incorrect responses; it is fast, local-optimum-free, and statistically consistent. In the past few years, spectral techniques have been used on real-world problems involving latent variables in dynamical systems, computer vision, and natural language processing. Our results suggest that the parameters learned by the spectral algorithm can replace the parameters learned by EM; the results of our study show that the spectral algorithm can improve knowledge tracing parameter- fitting time significantly while maintaining the same prediction accuracy, or help to improve accuracy while still keeping parameter-fitting time equivalent to EM. Consider the problem of approximating the optimal policy of a Markov decision process (MDP) by sampling state transitions. In contrast to existing reinforcement learning methods that are based on successive approximations to the nonlinear Bellman equation, we propose a Primal-Dual @math Learning method in light of the linear duality between the value and policy. The @math learning method is model-free and makes primal-dual updates to the policy and value vectors as new data are revealed. For infinite-horizon undiscounted Markov decision process with finite state space @math and finite action space @math , the @math learning method finds an @math -optimal policy using the following number of sample transitions @math where @math is an upper bound of mixing times across all policies and @math is a parameter characterizing the range of stationary distributions across policies. The @math learning method also applies to the computational problem of MDP where the transition probabilities and rewards are explicitly given as the input. In the case where each state transition can be sampled in @math time, the @math learning method gives a sublinear-time algorithm for solving the averaged-reward MDP. Scholars are increasingly citing electronic “web references” which are not preserved in libraries or full text archives. WebCite is a new standard for citing web references. To “webcite” a document involves archiving the cited Web page through www.webcitation.org and citing the WebCite permalink instead of (or in addition to) the unstable live Web page. This journal has amended its “instructions for authors” accordingly, asking authors to archive cited Web pages before submitting a manuscript. Almost 200 other journals are already using the system. We discuss the rationale for WebCite, its technology, and how scholars, editors, and publishers can benefit from the service. Citing scholars initiate an archiving process of all cited Web references, ideally before they submit a manuscript. Authors of online documents and websites which are expected to be cited by others can ensure that their work is permanently available by creating an archived copy using WebCite and providing the citation information including the WebCite link on their Web document(s). Editors should ask their authors to cache all cited Web addresses (Uniform Resource Locators, or URLs) “prospectively” before submitting their manuscripts to their journal. Editors and publishers should also instruct their copyeditors to cache cited Web material if the author has not done so already. Finally, WebCite can process publisher submitted “citing articles” (submitted for example as eXtensible Markup Language [XML] documents) to automatically archive all cited Web pages shortly before or on publication. Finally, WebCite can act as a focussed crawler, caching retrospectively references of already published articles. Copyright issues are addressed by honouring respective Internet standards (robot exclusion files, no-cache and no-archive tags). Long-term preservation is ensured by agreements with libraries and digital preservation organizations. The resulting WebCite Index may also have applications for research assessment exercises, being able to measure the impact of Web services and published Web documents through access and Web citation metrics. @PARASPLIT [J Med Internet Res 2005;7(5):e60] 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 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 era of Big Data has spawned unprecedented interests in developing hashing algorithms for efficient storage and fast nearest neighbor search. Most existing work learn hash functions that are numeric quantizations of feature values in projected feature space. In this work, we propose a novel hash learning framework that encodes feature's rank orders instead of numeric values in a number of optimal low-dimensional ranking subspaces. We formulate the ranking subspace learning problem as the optimization of a piece-wise linear convex-concave function and present two versions of our algorithm: one with independent optimization of each hash bit and the other exploiting a sequential learning framework. Our work is a generalization of the Winner-Take-All (WTA) hash family and naturally enjoys all the numeric stability benefits of rank correlation measures while being optimized to achieve high precision at very short code length. We compare with several state-of-the-art hashing algorithms in both supervised and unsupervised domain, showing superior performance in a number of data sets. We introduce a class of MPDs which greatly simplify Reinforcement Learning. They have discrete state spaces and continuous control spaces. The controls have the effect of rescaling the transition probabilities of an underlying Markov chain. A control cost penalizing KL divergence between controlled and uncontrolled transition probabilities makes the minimization problem convex, and allows analytical computation of the optimal controls given the optimal value function. An exponential transformation of the optimal value function makes the minimized Bellman equation linear. Apart from their theoretical significance, the new MDPs enable efficient approximations to traditional MDPs. Shortest path problems are approximated to arbitrary precision with largest eigenvalue problems, yielding an O (n) algorithm. Accurate approximations to generic MDPs are obtained via continuous embedding reminiscent of LP relaxation in integer programming. Off-policy learning of the optimal value function is possible without need for state-action values; the new algorithm (Z-learning) outperforms Q-learning.