nils-herrmann/clean_scirepeval huggingface dataset:
Characterizing distributions of stochastic processes by linear operators

This report describes how the finite-dimensional marginal distributions of a stochastic process (Ω,A, P, (Xt)t∈T ) with values in an arbitrary measurable space (E,B), where T = N or T = R≥0, can be calculated with linear operators. In the discrete-time, discrete-observation case, we construct a family of linear operators (τa)a∈E on a suitable real vector space V , such that any probability P (X0 = a0, . . . , Xn−1 = an−1) can be obtained by evaluating a product of matrices and vectors of the form στan−1 · · · τa0v0, where v0 ∈ V is a suitable starting vector and σ is the vector (1, . . . , 1). Conversely, necessary and sufficient conditions are given for algebraic structures (V, (τa)a∈E, v0) to describe a distribution of a process. Thus, a 1–1 correspondence between certain algebraic structures and distributions of discrete processes is found. These results are generalized to continuous time and arbitrary measurable spaces. All in all, one obtains a novel access to stochastic processes, by showing a way to model their distributions purely by means from linear algebra. key words: stochastic processes, distributions, observable operator models Zusammenfassung. In diesem Report wird beschrieben, wie die endlichdimensionalen Randverteilungen eines stochastischen Prozesses (Ω,A, P, (Xt)t∈T ) mit Werten in einem beliebigen Meßraum (E,B), wobei T = N oder T = R≥0, mit linearen Operatoren berechnet werden können. Im Falle diskreter Zeit und endlichen Meßraumes konstruieren wir eine Familie linearer Operatoren (τa)a∈E auf einem geeigneten reellen Vektorraum V , so dass Wahrscheinlichkeiten der Art P (X0 = a0, . . . , Xn−1 = an−1) durch die Auswertung eines Matrizen/Vektorproduktes der Form στan−1 · · · τa0v0 erhalten werden, wobei v0 ∈ V ein geeigneter Startvektor und σ der Vektor (1, . . . , 1) ist. Umgekehrt werden hinreichende und notwendige Bedingungen für eine algebraische Struktur (V, (τa)a∈E, v0) angegeben, dass diese in der erwähnten Weise die Verteilung eines Prozesses beschreibt. So wird eine 1 – 1 Beziehung zwischen bestimmten algebraischen Strukturen und Verteilungen diskreter Prozesse aufgewiesen. Diese Ergebnisse werden sodann auf kontinuierliche Zeit und beliebige Messräume verallgemeinert. Alles in allem erhält man einen neuen Zugang zu stochastischen Prozessen, indem deren Verteilungen mit Mitteln der linearen Algebra modelliert werden. Stichwörter: stochastische Prozesse, Verteilungen, observable operator models
Action selection for stochastic, delayed reward ?

The paper gives a novel account of quick decision making for maximising delayed reward in a stochastic world. The approach rests on observable operator models of stochastic systems, which generalize hidden Markov models. A particular kind of decision situations is outlined, and an algorithm is presented which allows to estimate the probability of future reward with a computational cost of only O(im), where i is the number of action alternatives and m is the model dimension.
A short introduction to observable operator models of stochastic processes

The article describes a new formal approach to model discrete stochastic processes, called observable operator models (OOMs). It is shown how hidden Markov models (HMMs) can be properly generalized to OOMs. These OOMs afiord both mathematical simplicity and algorithmic e‐ciency, where HMMs exhibit neither. The observable operator idea also leads to an abstract, information-theoretic representation of stationary stochastic processes. It is shown how any such process can be uniquely characterized by linear, observable operators, yielding an abstract OOM of the process. All in all, observable operators open a lucid, general, and computationally extremely powerful avenue to stochastic processes.
Self-organization of feature detectors in time sequences (SOFT)-a neural network approach to multidimensional signal analysis

We present a neural network algorithm for self-organization of feature detectors in time sequences (SOFT) based on the mathematical concept of transient attractors. It evaluates local phase space volume contraction as an indicator for good short-term predictability. SOFT supports category formation and event detection in multidimensional time sequences by linking together neural function approximation and principal component analysis. Possible extensions of the algorithm including iteration and vector quantization procedures for further data analysis are discussed.
A framework for plan execution in behavior-based robots

We present a conceptual architecture for autonomous robots that integrates behavior-based and goal-directed action as by following a traditional action plan. Dual dynamics is the formalism for describing behavior-based action. Partial-order propositional plans are used as a basis for acting goal-directedly; the concept is suitable for using other planning methods and plan formats, though. We describe the corresponding action and plan representations at the plan side and at the behavior side. Moreover, we demonstrate how behavior-based action is biased towards executing a plan and how information from the behavior side is fed back to the plan side to determine progress in the plan execution.
A short introduction to observable operator models of discrete stochastic processes ∗

The article describes a new formal approach to model discrete stochastic processes, called observable operator models (OOMs). It is shown how hidden Markov models (HMMs) can be properly generalized to OOMs. These OOMs afford both mathematical simplicity and algorithmic efficiency, where HMMs exhibit neither. The observable operator idea also leads to an abstract, information-theoretic representation of stationary, discrete stochastic processes. It is shown how any such process can be uniquely characterized by its abstract observable operators, yielding an abstract OOM of the process. All in all, observable operators open a lucid, general, and computationally extremely powerful avenue to discrete stochastic processes.
Observable operator models II: Interpretable models and model induction

This article is a direct continuation of the tech report Observable Operator Models and Conditioned Continuation Representations, Ar-beitspapiere der GMD 1043, 1997. While the former paper described the mathematical theory of OOMs, the present article presents techniques for practical applications. A standardized graphical representation of OOM-generated processes is developed, which helps a lot to gain an intuitive grasp on relevant phenomena. The main contribution is an eecient constructive algorithm for the induction of OOMs from data.
The Dual Dynamics Design Scheme for Behavior based Robots A Tutorial

This paper is a tutorial on a particular method for designing behavior based robots the dual dynamics DD scheme The DD scheme guides the speci cation of multi level control architectures in a format of di erential equations DD design is characterized by two principal properties First behaviors are construed as dynamical systems which consist of two subsystems hence the name dual dynamics One subsystem generates the behavior s dynamics proper the other is responsible for activating and de activating the behavior The second principal property is that higher levels in the control architecture do not directly call lower level behaviors to execute Rather a higher level behavior can con gure the entire lower level which thereafter can operate fully on its own without ongoing supervision by the higher level Zusammenfassung Dies ist ein Tutorial f ur das Dual Dynamics DD Entwurfs schema eine spezielle Entwurfsmethode f ur behavior basierte Roboter Das DD Schema gibt Anleitungen zur Spezi kation vonmehrschichtigen Kontrollarchitekturen durch Di er entialgleichungen Das Schema ist durch zwei haupts achliche Eigenschaften gekennzeich net Erstens werden Behaviors als dynamische Systeme modelliert die jeweils aus zwei Subsystemen bestehen daher der Name Dual Dynamics Das erste dieser Subsysteme generiert die eigentliche Dynamik des Behaviors w ahrend das zweite seine Aktivierung bzw Deaktivierung regelt Die zweite Haupteigenschaft besteht darin da Behaviors auf h oheren Ebenen in der Kontrollarchitektur Behaviors auf tieferen Ebenen nicht direkt aufrufen Vielmehr kon guriert ein h oheres Behavior die ganze n achsttiefe Ebene von Behaviors Diese tiefere Ebene operiert danach als Ganze selbst andig ohne Uberwa chung durch die h ohere Ebene
Transient attractors: Re-recognizable regularities in empirical time series

A common rst step in analyzing empirical, continuous time series is to transform them into a symbol sequence. This requires to de ne re-recognizable entities in the original data, which can be labelled by symbols. Two families of classical candidates for such entities are attractors and volume cells in phase space. They have complementary merits. This article describes a third kind of nameable entities, transient attractors, which combine and volume cells and their respective merits. An algorithm for the practical extraction of transient attractors from empirical data is sketched.
Dynamic Symbol Systems : An Introduction to the Local Model

Dynamic symbol systems (DSS) are a class of dynamic systems especially developed for modeling situated agents. They combine a symbolic format of representation with a selforganizing dynamics. The theory can be used for theoretical purposes, as a discrete, approximative reconstruction of continuous dynamic systems. It can also be used for the practical design of multi-granular information processing systems, since it is formulated in algorithmic terms. Furthermore, as processing on a conceptual level is concerned, the dynamic system perspective suggests answers to some questions that are hard for logic-oriented approaches. All in all, DSS contributes to bridging the gap between dynamics-oriented, bottom-up techniques, and representation-oriented, top-down perspectives in AI. The paper gives an informal introduction to the part of DSS theory concerned with local phenomena, while the global part of the theory is very briefly sketched. October 1994 draft version submitted to AISB-95
Identi cation of Behaviors in an Agent's Phase Space

This paper describes a method for analyzing the behavior of an autonomous robot. The robot is viewed as a continuous, stochastic dynamical system. The analysis starts from an empirical phase portrait. In a rst stage, elementary regularities are detected. These regularities, called transient attractors, combine properties of attractors with properties of partition cells of phase space. As the system trajectory passes through these regularities repeatedly, a sequence of identi able events is produced, which can be interpreted as a symbol sequence. This sequence is further analyzed in the second stage, where a nite description of temporal regularities within it is constructed. This description comes in the format of a variety of nite-state automata. In a third stage, higher-order regularities in this nite-state-like description are identi ed. This yields a hierarchic behavior model. At all stages, regularities are de ned using criteria of maximal local predictability. Thus, the entire method can be seen as an information theoretic approach to bridging the gap between the non-symbolic, quantitative level of robots and higher-level symbolic models.  Es wird eine Methode zur Analyse des Verhaltens von autonomen Robotern vorgestellt. Letztere werden als kontinuierliche, stochastische, dynamische Systeme aufgefa t. Die Analyse geht von einem empirisch bestimmten Phasenportrait aus. In einer ersten Stufe werden darin elementare Regularit aten identi ziert, die ich transiente Attraktoren nenne. Sie kombinieren Eigenschaften von Attraktoren mit Eigenschaften von Partitionszellen in Phasenraumen. Indem die Systemtrajektorie wiederholt durch diese Regularitaten hindurchgeht, wird eine Ereigniskette bestimmt, die formal als Symbolsequenz aufgefa t werden kann. In einer zweiten Analysestufe wird eine endliche Beschreibung von temporalen Regularitaten in dieser Sequenz vorgenommen. Diese Beschreibung ist formal verwandt mit endlichen Automaten. In einer dritten Analysestufe werden in dieser automatenahnlichen Beschreibung Regularitaten hoherer Ordnung identi ziert. Es ergibt sich schlie lich insgesamt ein hierarchisches Verhaltensmodell. In allen Analysestufen werden die jeweiligen Regularitaten durch lokale Optimalit atskriterien der Proze vorhersagbarkeit bestimmt. Der gesamte Analyseproze erbringt so eine informationstheoretisch orientierte Verbindung der quantitativen Beschreibungsebene mit h oheren symbolischen Modellen.
Learning Causally Linked Markov Random Fields

We describe a learning procedure for a generative model that contains a hidden Markov Random Field (MRF) which has directed connections to the observable variables. The learning procedure uses a variational approximation for the posterior distribution over the hidden variables. Despite the intractable partition function of the MRF, the weights on the directed connections and the variational approximation itself can be learned by maximizing a lower bound on the log probability of the observed data. The parameters of the MRF are learned by using the mean field version of contrastive divergence . We show that this hybrid model simultaneously learns parts of objects and their inter-relationships from intensity images. We discuss the extension to multiple MRF’s linked into in a chain graph by directed connections.
Embedding viaclustering: Using spectral information toguidedimensionality reduction

We describe anapproach toimprove iterative di- mensionality reduction methods byusing information contained intheleading eigenvectors ofa dataaffinity matrix. Using an insight fromtheareaofspectral clustering, we suggest modifying thegradient ofaniterative method, sothatlatent spaceelements belonging tothesamecluster areencouraged to moveinsimilar directions during optimization. Wealso describe waytoachieve this without actually having toexplicitly perform aneigendecomposition. Preliminary experiments showthat our approach makesitpossible tospeed upiterative methods and helps themtofind better local minima oftheir objective function.
What kind of graphical model is the brain?

If neurons are treated as latent variables, our visual systems are non-linear, densely-connected graphical models containing billions of variables and thousands of billions of parameters. Current algorithms would have difficulty learning a graphical model of this scale. Starting with an algorithm that has difficulty learning more than a few thousand parameters, I describe a series of progressively better learning algorithms all of which are designed to run on neuron-like hardware. The latest member of this series can learn deep, multi-layer belief nets quite rapidly. It turns a generic network with three hidden layers and 1:7 million connections into a very good generative model of handwritten digits. After learning, the model gives classification performance that is comparable to the best discriminative methods.
On Contrastive Divergence Learning

Maximum-likelihood (ML) learning of Markov random fields is challenging because it requires estimates of averages that have an exponential number of terms. Markov chain Monte Carlo methods typically take a long time to converge on unbiased estimates, but Hinton (2002) showed that if the Markov chain is only run for a few steps, the learning can still work well and it approximately minimizes a different function called “contrastive divergence” (CD). CD learning has been successfully applied to various types of random fields. Here, we study the properties of CD learning and show that it provides biased estimates in general, but that the bias is typically very small. Fast CD learning can therefore be used to get close to an ML solution and slow ML learning can then be used to fine-tune the CD solution. Consider a probability distribution over a vector x (assumed discrete w.l.o.g.) and with parameters W p(x;W) = 1 Z(W) e (1) where Z(W) = ∑ x e −E(x;W) is a normalisation constant and E(x;W) is an energy function. This class of random-field distributions has found many practical applications (Li, 2001; Winkler, 2002; Teh et al., 2003; He et al., 2004). Maximum-likelihood (ML) learning of the parameters W given an iid sample X = {xn}n=1 can be done by gradient ascent: W = W + η ∂L(W;X ) ∂W ∣
Inferring Motor Programs from Images of Handwritten Digits

We describe a generative model for handwritten digits that uses two pairs of opposing springs whose stiffnesses are controlled by a motor program. We show how neural networks can be trained to infer the motor programs required to accurately reconstruct the MNIST digits. The inferred motor programs can be used directly for digit classification, but they can also be used in other ways. By adding noise to the motor program inferred from an MNIST image we can generate a large set of very different images of the same class, thus enlarging the training set available to other methods. We can also use the motor programs as additional, highly informative outputs which reduce overfitting when training a feed-forward classifier.
Probabilistic sequential independent components analysis

Under-complete models, which derive lower dimensional representations of input data, are valuable in domains in which the number of input dimensions is very large, such as data consisting of a temporal sequence of images. This paper presents the under-complete product of experts (UPoE), where each expert models a one-dimensional projection of the data. Maximum-likelihood learning rules for this model constitute a tractable and exact algorithm for learning under-complete independent components. The learning rules for this model coincide with approximate learning rules proposed earlier for under-complete independent component analysis (UICA) models. This paper also derives an efficient sequential learning algorithm from this model and discusses its relationship to sequential independent component analysis (ICA), projection pursuit density estimation, and feature induction algorithms for additive random field models. This paper demonstrates the efficacy of these novel algorithms on high-dimensional continuous datasets.
Exponential Family Harmoniums with an Application to Information Retrieval

Directed graphical models with one layer of observed random variables and one or more layers of hidden random variables have been the dominant modelling paradigm in many research fields. Although this approach has met with considerable success, the causal semantics of these models can make it difficult to infer the posterior distribution over the hidden variables. In this paper we propose an alternative two-layer model based on exponential family distributions and the semantics of undirected models. Inference in these "exponential family harmoniums" is fast while learning is performed by minimizing contrastive divergence. A member of this family is then studied as an alternative probabilistic model for latent semantic indexing. In experiments it is shown that they perform well on document retrieval tasks and provide an elegant solution to searching with keywords.
Neighbourhood Components Analysis

In this paper we propose a novel method for learning a Mahalanobis distance measure to be used in the KNN classification algorithm. The algorithm directly maximizes a stochastic variant of the leave-one-out KNN score on the training set. It can also learn a low-dimensional linear embedding of labeled data that can be used for data visualization and fast classification. Unlike other methods, our classification model is non-parametric, making no assumptions about the shape of the class distributions or the boundaries between them. The performance of the method is demonstrated on several data sets, both for metric learning and linear dimensionality reduction.
Reinforcement Learning with Factored States and Actions

A novel approximation method is presented for approximating the value function and selecting good actions for Markov decision processes with large state and action spaces. The method approximates state-action values as negative free energies in an undirected graphical model called a product of experts. The model parameters can be learned efficiently because values and derivatives can be efficiently computed for a product of experts. Actions can be found even in large factored action spaces by the use of Markov chain Monte Carlo sampling. Simulation results show that the product of experts approximation can be used to solve large problems. In one simulation it is used to find actions in action spaces of size 240.
Multiple Relational Embedding

We describe a way of using multiple different types of similarity relationship to learn a low-dimensional embedding of a dataset. Our method chooses different, possibly overlapping representations of similarity by individually reweighting the dimensions of a common underlying latent space. When applied to a single similarity relation that is based on Euclidean distances between the input data points, the method reduces to simple dimensionality reduction. If additional information is available about the dataset or about subsets of it, we can use this information to clean up or otherwise improve the embedding. We demonstrate the potential usefulness of this form of semi-supervised dimensionality reduction on some simple examples.
A Mode-Hopping MCMC sampler

One of the main shortcomings of Markov chain Monte Carlo samplers is their inability to mix between modes of the target distribution. In this paper we show that advance knowledge of the location of these modes can be incorporated into the MCMC sampler by introducing mode-hopping moves that satisfy detailed balance. The proposed sampling algorithm explores local mode structure through local MCMC moves (e.g. diffusion or Hybrid Monte Carlo) but in addition also represents the relative strengths of the different modes correctly using a set of global moves. This “mode-hopping” MCMC sampler can be viewed as a generalization of the darting method .
Bethe free energy and contrastive divergence approximations for undirected graphical models

As the machine learning community tackles more complex and harder problems, the graphical models needed to solve such problems become larger and more complicated. As a result performing inference and learning exactly for such graphical models become ever more expensive, and approximate inference and learning techniques become ever more prominent. 
There are a variety of techniques for approximate inference and learning in the literature. This thesis contributes some new ideas in the products of experts (PoEs) class of models (Hinton, 2002), and the Bethe free energy approximations (Yedidia et al., 2001). 
For PoEs, our contribution is in developing new PoE models for continuous-valued domains. We developed RBMrate, a model for discretized continuous-valued data. We applied it to face recognition to demonstrate its abilities. We also developed energy-based models (EBMs)—flexible probabilistic models where the building blocks consist of energy terms computed using a feed-forward network. We show that standard square noiseless independent components analysis (ICA) (Bell and Sejnowski, 1995) can be viewed as a restricted form of EBMs. Extending this relationship with ICA, we describe sparse and over-complete representations of data where the inference process is trivial since it is simply an EBM. 
For Bethe free energy approximations, our contribution is a theory relating belief propagation and iterative scaling. We show that both belief propagation and iterative scaling updates can be derived as fixed point equations for constrained minimization of the Bethe free energy. This allows us to develop a new algorithm to directly minimize the Bethe free energy, and to apply the Bethe free energy to learning in addition to inference. We also describe improvements to the efficiency of standard learning algorithms for undirected graphical models (Jirousek and Preucil, 1995).