nils-herrmann/clean_scirepeval huggingface dataset:
A Pricing Formula for Delayed Claims: Appreciating the Past to Value the Future

We consider the valuation of contingent claims with delayed dynamics in a Black \& Scholes complete market model. We find a pricing formula that can be decomposed into terms reflecting the market values of the past and the present, showing how the valuation of future cashflows cannot abstract away from the contribution of the past. As a practical application, we provide an explicit expression for the market value of human capital in a setting with wage rigidity.
The Benefit of Multitask Representation Learning

We discuss a general method to learn data representations from multiple tasks. We provide a justification for this method in both settings of multitask learning and learning-to-learn. The method is illustrated in detail in the special case of linear feature learning. Conditions on the theoretical advantage offered by multitask representation learning over independent task learning are established. In particular, focusing on the important example of half-space learning, we derive the regime in which multitask representation learning is beneficial over independent task learning, as a function of the sample size, the number of tasks and the intrinsic data dimensionality. Other potential applications of our results include multitask feature learning in reproducing kernel Hilbert spaces and multilayer, deep networks.
Modeling of the meaning: computational interpreting and understanding of natural language fragments

In this introductory article we present the basics of an approach to implementing computational interpreting of natural language aiming to model the meanings of words and phrases. Unlike other approaches, we attempt to define the meanings of text fragments in a composable and computer interpretable way. We discuss models and ideas for detecting different types of semantic incomprehension and choosing the interpretation that makes most sense in a given context. Knowledge representation is designed for handling context-sensitive and uncertain / imprecise knowledge, and for easy accommodation of new information. It stores quantitative information capturing the essence of the concepts, because it is crucial for working with natural language understanding and reasoning. Still, the representation is general enough to allow for new knowledge to be learned, and even generated by the system. The article concludes by discussing some reasoning-related topics: possible approaches to generation of new abstract concepts, and describing situations and concepts in words (e.g. for specifying interpretation difficulties).
Inverse transport problems in quantitative PAT for molecular imaging

Fluorescence photoacoustic tomography (fPAT) is a molecular imaging modality that combines photoacoustic tomography with fluorescence imaging to obtain high-resolution imaging of fluorescence distributions inside heterogeneous media. The objective of this work is to study inverse problems in the quantitative step of fPAT where we intend to reconstruct physical coefficients in a coupled system of radiative transport equations using internal data recovered from ultrasound measurements. We derive uniqueness and stability results on the inverse problems and develop some efficient algorithms for image reconstructions. Numerical simulations based on synthetic data are presented to validate the theoretical analysis. The results we present here complement these in Ren K and Zhao H (2013 ) on the same problem but in the diffusive regime.
Classification and Regression Using an Outer Approximation Projection-Gradient Method

This paper deals with sparse feature selection and grouping for classification and regression. The classification or regression problems under consideration consists of minimizing a convex empirical risk function subject to an <inline-formula><tex-math notation="LaTeX">$\ell ^1$</tex-math></inline-formula> constraint, a pairwise <inline-formula> <tex-math notation="LaTeX">$\ell ^\infty$</tex-math></inline-formula> constraint, or a pairwise <inline-formula> <tex-math notation="LaTeX">$\ell ^1$</tex-math></inline-formula> constraint. Existing work, such as the Lasso formulation, has focused mainly on Lagrangian penalty approximations, which often require <italic>ad hoc</italic> or computationally expensive procedures to determine the penalization parameter. We depart from this approach and address the constrained problem directly via a splitting method. The structure of the method is that of the classical gradient-projection algorithm, which alternates a gradient step on the objective and a projection step onto the lower level set modeling the constraint. The novelty of our approach is that the projection step is implemented via an outer approximation scheme in which the constraint set is approximated by a sequence of simple convex sets consisting of the intersection of two half-spaces. Convergence of the iterates generated by the algorithm is established for a general smooth convex minimization problem with inequality constraints. Experiments on both synthetic and biological data show that our method outperforms penalty methods.
Time-scale analysis of co-movement in EU sovereign bond markets

We study the co-movement of the 10-year sovereign bond yields of 11 EU countries. Our analysis is focused mainly on changes in co-movement during the financial crisis period, especially around two significant dates - the fall of Lehman Brothers, September 15, 2008, and the announcement of the increase of Greece's public deficit on October 20, 2009. We study co-movement dynamics using wavelet analysis, which allows us to observe how co-movement changes across frequencies and over time. We divide the countries into three groups: the core of the Eurozone, the periphery of the Eurozone and the states outside the Eurozone. The results indicate that co-movement decreased considerably during the crisis period for all country pairs but that there are significant differences among the groups. Furthermore, we demonstrate that the co-movement of bond yields is frequency (scale) dependent.
Information-based inference for singular models and finite sample sizes

A central problem in statistics is model selection, the choice between competing models of a stochastic process whose observables are corrupted by noise. In the information-based paradigm of inference, model selection is performed by estimating the predictive performance of the com- peting models. The candidate model with the best estimated predictive performance is selected. Information-based inference is dependent on the accuracy of the estimate of the predictive complexity, a measure of the flexibility of the model in fitting the data. A large-sample-size approximation for the performance is the Akaike Information Criterion (AIC). The AIC approximation fails in a wide range of important applications, either significantly under or over-estimating the complexity. We introduce an improved approximation for the complexity which we use to define a new information criterion: the frequentist information criterion (FIC). FIC extends the applicability of information-based infer- ence to the finite-sample-size regime of regular models and to singular models. We demonstrate the power of the approach in a number of example problems.
Classical random walks over complex networks and network complexity

In this paper we view the steady states of classical random walks over complex networks with an arbitrary degree distribution as states in thermal equilibrium. By identifying the distribution of states as a canonical ensemble, we are able to define the temperature and the Hamiltonian for the random walk systems. We then calculate the Helmholtz free energy, the average energy, and the entropy for the thermal equilibrium states. The results shows equipartition of energy for the average energy. The entropy is found to consist of two parts. The first part decreases as the number of walkers increases. The second part of the entropy depends solely on the topology of the network, and will increase when more edges or nodes are added to the network. We compare the topological part of entropy with some of the network descriptors and find that the topological entropy could be used as a measure of network complexity. In addition, we discuss the scenario that a walker has a prior probability of resting on the same node at the next time step, and find that the effect of the prior resting probabilities is equivalent to increasing the degree for every node in the network.
Pareto Smoothed Importance Sampling

Importance weighting is a general way to adjust Monte Carlo integration to account for draws from the wrong distribution, but the resulting estimate can be noisy when the importance ratios have a heavy right tail. This routinely occurs when there are aspects of the target distribution that are not well captured by the approximating distribution, in which case more stable estimates can be obtained by modifying extreme importance ratios. We present a new method for stabilizing importance weights using a generalized Pareto distribution fit to the upper tail of the distribution of the simulated importance ratios. The method, which empirically performs better than existing methods for stabilizing importance sampling estimates, includes stabilized effective sample size estimates, Monte Carlo error estimates and convergence diagnostics.
Pushdown control-flow analysis for free

Traditional control-flow analysis (CFA) for higher-order languages introduces spurious connections between callers and callees, and different invocations of a function may pollute each other's return flows. Recently, three distinct approaches have been published that provide perfect call-stack precision in a computable manner: CFA2, PDCFA, and AAC. Unfortunately, implementing CFA2 and PDCFA requires significant engineering effort. Furthermore, all three are computationally expensive. For a monovariant analysis, CFA2 is in O(2^n), PDCFA is in O(n^6), and AAC is in O(n^8). In this paper, we describe a new technique that builds on these but is both straightforward to implement and computationally inexpensive. The crucial insight is an unusual state-dependent allocation strategy for the addresses of continuations. Our technique imposes only a constant-factor overhead on the underlying analysis and costs only O(n^3) in the monovariant case. We present the intuitions behind this development, benchmarks demonstrating its efficacy, and a proof of the precision of this analysis.
Learning Fair Classifiers

Automated data-driven decision systems are ubiquitous across a wide variety of online services, from online social networking and e-commerce to e-government. These systems rely on complex learning methods and vast amounts of data to optimize the service functionality, satisfaction of the end user and profitability. However, there is a growing concern that these automated decisions can lead to user discrimination, even in the absence of intent, leading to a lack of fairness, i.e., their outcomes have a disproportionally large adverse impact on particular groups of people sharing one or more sensitive attributes (e.g., race, sex). In this paper, we introduce a flexible mechanism to design fair classifiers in a principled manner. Then, we instantiate this mechanism on three well-known classifiers -- logistic regression, hinge loss and linear and nonlinear support vector machines. Experiments on both synthetic and real-world data show that our mechanism allows for a fine-grained control of the level of fairness, often at a minimal cost in terms of accuracy, and it provides more flexibility than alternatives.
Perturbed Iterate Analysis for Asynchronous Stochastic Optimization

We introduce and analyze stochastic optimization methods where the input to each gradient update is perturbed by bounded noise. We show that this framework forms the basis of a unified approach to analyze asynchronous implementations of stochastic optimization algorithms.In this framework, asynchronous stochastic optimization algorithms can be thought of as serial methods operating on noisy inputs. Using our perturbed iterate framework, we provide new analyses of the Hogwild! algorithm and asynchronous stochastic coordinate descent, that are simpler than earlier analyses, remove many assumptions of previous models, and in some cases yield improved upper bounds on the convergence rates. We proceed to apply our framework to develop and analyze KroMagnon: a novel, parallel, sparse stochastic variance-reduced gradient (SVRG) algorithm. We demonstrate experimentally on a 16-core machine that the sparse and parallel version of SVRG is in some cases more than four orders of magnitude faster than the standard SVRG algorithm.
Perceptron like Algorithms for Online Learning to Rank

Perceptron is a classic online algorithm for learning a classification function. In this paper, we provide a novel extension of the perceptron algorithm to the learning to rank problem in information retrieval. We consider popular listwise performance measures such as Normalized Discounted Cumulative Gain (NDCG) and Average Precision (AP). A modern perspective on perceptron for classification is that it is simply an instance of online gradient descent (OGD), during mistake rounds, using the hinge loss function. Motivated by this interpretation, we propose a novel family of listwise, large margin ranking surrogates. Members of this family can be thought of as analogs of the hinge loss. Exploiting a certain self-bounding property of the proposed family, we provide a guarantee on the cumulative NDCG (or AP) induced loss incurred by our perceptron-like algorithm. We show that, if there exists a perfect oracle ranker which can correctly rank each instance in an online sequence of ranking data, with some margin, the cumulative loss of perceptron algorithm on that sequence is bounded by a constant, irrespective of the length of the sequence. This result is reminiscent of Novikoff's convergence theorem for the classification perceptron. Moreover, we prove a lower bound on the cumulative loss achievable by any deterministic algorithm, under the assumption of existence of perfect oracle ranker. The lower bound shows that our perceptron bound is not tight, and we propose another, \emph{purely online}, algorithm which achieves the lower bound. We provide empirical results on simulated and large commercial datasets to corroborate our theoretical results.
A Randomized Rounding Algorithm for Sparse PCA

We present and analyze a simple, two-step algorithm to approximate the optimal solution of the sparse PCA problem. In the proposed approach, we first solve an ℓ1-penalized version of the NP-hard sparse PCA optimization problem and then we use a randomized rounding strategy to sparsify the resulting dense solution. Our main theoretical result guarantees an additive error approximation and provides a tradeoff between sparsity and accuracy. Extensive experimental evaluation indicates that the proposed approach is competitive in practice, even compared to state-of-the-art toolboxes such as Spasm.
Continuous control with deep reinforcement learning

We adapt the ideas underlying the success of Deep Q-Learning to the continuous action domain. We present an actor-critic, model-free algorithm based on the deterministic policy gradient that can operate over continuous action spaces. Using the same learning algorithm, network architecture and hyper-parameters, our algorithm robustly solves more than 20 simulated physics tasks, including classic problems such as cartpole swing-up, dexterous manipulation, legged locomotion and car driving. Our algorithm is able to find policies whose performance is competitive with those found by a planning algorithm with full access to the dynamics of the domain and its derivatives. We further demonstrate that for many of the tasks the algorithm can learn policies end-to-end: directly from raw pixel inputs.
Can You Hear the Shape of a Market? Geometric Arbitrage and Spectral Theory

Utilizing gauge symmetries, the Geometric Arbitrage Theory reformulates any asset model, allowing for arbitrage by means of a stochastic principal fibre bundle with a connection whose curvature measures the “instantaneous arbitrage capability”. The cash flow bundle is the associated vector bundle. The zero eigenspace of its connection Laplacian parameterizes all risk-neutral measures equivalent to the statistical one. A market satisfies the No-Free-Lunch-with-Vanishing-Risk (NFLVR) condition if and only if 0 is in the discrete spectrum of the Laplacian. The Jarrow–Protter–Shimbo theory of asset bubbles and their classification and decomposition extend to markets not satisfying the NFLVR. Euler’s characteristic of the asset nominal space and non-vanishing of the homology group of the cash flow bundle are both topological obstructions to NFLVR.
Bayesian Optimal Design for Ordinary Differential Equation Models With Application in Biological Science

Bayesian optimal design is considered for experiments where the response distribution depends on the solution to a system of nonlinear ordinary differential equations. The motivation is an experiment to estimate parameters in the equations governing the transport of amino acids through cell membranes in human placentas. Decision-theoretic Bayesian design of experiments for such nonlinear models is conceptually very attractive, allowing the formal incorporation of prior knowledge to overcome the parameter dependence of frequentist design and being less reliant on asymptotic approximations. However, the necessary approximation and maximization of the, typically analytically intractable, expected utility results in a computationally challenging problem. These issues are further exacerbated if the solution to the differential equations is not available in closed-form. This article proposes a new combination of a probabilistic solution to the equations embedded within a Monte Carlo approximation to the expected utility with cyclic descent of a smooth approximation to find the optimal design. A novel precomputation algorithm reduces the computational burden, making the search for an optimal design feasible for bigger problems. The methods are demonstrated by finding new designs for a number of common models derived from differential equations, and by providing optimal designs for the placenta experiment.
Quasinormal modes of extremal black holes

The continued fraction method (also known as Leaver's method) is one of the most effective techniques used to determine the quasinormal modes of a black hole. For extremal black holes, however, the method does not work (since, in such a case, the event horizon is an irregular singular point of the associated wave equation). Fortunately, there exists a modified version of the method, devised by Onozawa et al. , which works for neutral massless fields around an extremal Reissner-Nordstrom black hole. In this paper, we generalize the ideas of Onozawa et al. to charged massless perturbations around an extremal Reissner-Nordstrom black hole and to neutral massless perturbations around an extremal Kerr black hole. Similarities and differences between the results of the original continued fraction method for near extremal black holes and the results of the new continued fraction method for extremal black holes are discussed.
BLC: Private Matrix Factorization Recommenders via Automatic Group Learning

We propose a privacy-enhanced matrix factorization recommender that exploits the fact that users can often be grouped together by interest. This allows a form of "hiding in the crowd" privacy. We introduce a novel matrix factorization approach suited to making recommendations in a shared group (or nym) setting and the BLC algorithm for carrying out this matrix factorization in a privacy-enhanced manner. We demonstrate that the increased privacy does not come at the cost of reduced recommendation accuracy.
Optimal trading strategies—a time series approach

Motivated by recent advances in the spectral theory of auto-covariance matrices, we are led to revisit a reformulation of Markowitz’ mean-variance portfolio optimization approach in the time domain. In its simplest incarnation it applies to a single traded asset and allows an optimal trading strategy to be found which—for a given return—is minimally exposed to market price fluctuations. The model is initially investigated for a range of synthetic price processes, taken to be either second order stationary, or to exhibit second order stationary increments. Attention is paid to consequences of estimating auto-covariance matrices from small finite samples, and auto-covariance matrix cleaning strategies to mitigate against these are investigated. Finally we apply our framework to real world data.
Resolving References to Objects in Photographs using the Words-As-Classifiers Model

A common use of language is to refer to visually present objects. Modelling it in computers requires modelling the link between language and perception. The "words as classifiers" model of grounded semantics views words as classifiers of perceptual contexts, and composes the meaning of a phrase through composition of the denotations of its component words. It was recently shown to perform well in a game-playing scenario with a small number of object types. We apply it to two large sets of real-world photographs that contain a much larger variety of types and for which referring expressions are available. Using a pre-trained convolutional neural network to extract image features, and augmenting these with in-picture positional information, we show that the model achieves performance competitive with the state of the art in a reference resolution task (given expression, find bounding box of its referent), while, as we argue, being conceptually simpler and more flexible.
Learning-Based Compressive Subsampling

The problem of recovering a structured signal x ∈ C<sup>p</sup> from a set of dimensionality-reduced linear measurements b = Ax arises in a variety of applications, such as medical imaging, spectroscopy, Fourier optics, and computerized tomography. Due to computational and storage complexity or physical constraints imposed by the problem, the measurement matrix A ∈ C<sup>n×p</sup> is often of the form A = P<sub>Ω</sub>Ψ for some orthonormal basis matrix Ψ ∈ C<sup>P×P</sup> and subsampling operator P<sub>Ω</sub> : C<sup>p</sup> → C<sup>n</sup> that selects the rows indexed by Ω. This raises the fundamental question of how best to choose the index set Ω in order to optimize the recovery performance. Previous approaches to addressing this question rely on nonuniform random subsampling using application-specific knowledge of the structure of x. In this paper, we instead take a principled learning-based approach in which affixed index set is chosen based on a set of training signals x<sub>1</sub>, . . . , x<sub>m</sub>. We formulate combinatorial optimization problems seeking to maximize the energy captured in these signals in an average-case or worst-case sense, and we show that these can be efficiently solved either exactly or approximately via the identification of modularity and submodularity structures. We provide both deterministic and statistical theoretical guarantees showing how the resulting measurement matrices perform on signals differing from the training signals, and we provide numerical examples showing our approach to be effective on a variety of data sets.
Quantifying the Information of the Prior and Likelihood in Parametric Bayesian Modeling

I suggest using a pair of metrics to quantify the information of the prior and likelihood functions within a parametric Bayesian model, one of which is closely related to the reference priors of Berger and Bernardo (Bernardo 1979, Berger and Bernardo 2009) and information measure introduced by Lindley (Lindley 1956). A Monte Carlo algorithm to estimate these metrics is developed and their properties are explored via a combination of theoretical results, simulations, and applications to public medical data sets. This combination of theoretical, empirical, and computational support provides evidence that these metrics may be useful diagnostic tools when performing a Bayesian analysis.