The Bradley-Terry-Luce (BTL) model is a classic and very popular statistical approach for eliciting a global ranking among a collection of items using pairwise comparison data. In applications in which the comparison outcomes are observed as a time series, it is often the case that data are non-stationary, in the sense that the true underlying ranking changes over time. In this paper we are concerned with localizing the change points in a high-dimensional BTL model with piece-wise constant parameters. We propose novel and practicable algorithms based on dynamic programming that can consistently estimate the unknown locations of the change points. We provide consistency rates for our methodology that depend explicitly on the model parameters, the temporal spacing between two consecutive change points and the magnitude of the change. We corroborate our findings with extensive numerical experiments and a real-life example.
相關內容
In the age of big data and interpretable machine learning, approaches need to work at scale and at the same time allow for a clear mathematical understanding of the method's inner workings. While there exist inherently interpretable semi-parametric regression techniques for large-scale applications to account for non-linearity in the data, their model complexity is still often restricted. One of the main limitations are missing interactions in these models, which are not included for the sake of better interpretability, but also due to untenable computational costs. To address this shortcoming, we derive a scalable high-order tensor product spline model using a factorization approach. Our method allows to include all (higher-order) interactions of non-linear feature effects while having computational costs proportional to a model without interactions. We prove both theoretically and empirically that our methods scales notably better than existing approaches, derive meaningful penalization schemes and also discuss further theoretical aspects. We finally investigate predictive and estimation performance both with synthetic and real data.
We study the costs and benefits of selling data to a competitor. Although selling all consumers' data may decrease total firm profits, there exist other selling mechanisms -- in which only some consumers' data is sold -- that render both firms better off. We identify the profit-maximizing mechanism, and show that the benefit to firms comes at a cost to consumers. We then construct Pareto-improving mechanisms, in which each consumers' welfare, as well as both firms' profits, increase. Finally, we show that consumer opt-in can serve as an instrument to induce firms to choose a Pareto-improving mechanism over a profit-maximizing one.
Autonomous robots are required to reason about the behaviour of dynamic agents in their environment. To this end, many approaches assume that causal models describing the interactions of agents are given a priori. However, in many application domains such models do not exist or cannot be engineered. Hence, the learning (or discovery) of high-level causal structures from low-level, temporal observations is a key problem in AI and robotics. However, the application of causal discovery methods to scenarios involving autonomous agents remains in the early stages of research. While a number of methods exist for performing causal discovery on time series data, these usually rely upon assumptions such as sufficiency and stationarity which cannot be guaranteed in interagent behavioural interactions in the real world. In this paper we are applying contemporary observation-based temporal causal discovery techniques to real world and synthetic driving scenarios from multiple datasets. Our evaluation demonstrates and highlights the limitations of state of the art approaches by comparing and contrasting the performance between real and synthetically generated data. Finally, based on our analysis, we discuss open issues related to causal discovery on autonomous robotics scenarios and propose future research directions for overcoming current limitations in the field.
In this paper, we study dimension reduction techniques for large-scale controlled stochastic differential equations (SDEs). The drift of the considered SDEs contains a polynomial term satisfying a one-sided growth condition. Such nonlinearities in high dimensional settings occur, e.g., when stochastic reaction diffusion equations are discretized in space. We provide a brief discussion around existence, uniqueness and stability of solutions. (Almost) stability then is the basis for new concepts of Gramians that we introduce and study in this work. With the help of these Gramians, dominant subspace are identified leading to a balancing related highly accurate reduced order SDE. We provide an algebraic error criterion and an error analysis of the propose model reduction schemes. The paper is concluded by applying our method to spatially discretized reaction diffusion equations.
Given a dataset on actions and resulting long-term rewards, a direct estimation approach fits value functions that minimize prediction error on the training data. Temporal difference learning (TD) methods instead fit value functions by minimizing the degree of temporal inconsistency between estimates made at successive time-steps. Focusing on finite state Markov chains, we provide a crisp asymptotic theory of the statistical advantages of this approach. First, we show that an intuitive inverse trajectory pooling coefficient completely characterizes the percent reduction in mean-squared error of value estimates. Depending on problem structure, the reduction could be enormous or nonexistent. Next, we prove that there can be dramatic improvements in estimates of the difference in value-to-go for two states: TD's errors are bounded in terms of a novel measure - the problem's trajectory crossing time - which can be much smaller than the problem's time horizon.
Learning decompositions of expensive-to-evaluate black-box functions promises to scale Bayesian optimisation (BO) to high-dimensional problems. However, the success of these techniques depends on finding proper decompositions that accurately represent the black-box. While previous works learn those decompositions based on data, we investigate data-independent decomposition sampling rules in this paper. We find that data-driven learners of decompositions can be easily misled towards local decompositions that do not hold globally across the search space. Then, we formally show that a random tree-based decomposition sampler exhibits favourable theoretical guarantees that effectively trade off maximal information gain and functional mismatch between the actual black-box and its surrogate as provided by the decomposition. Those results motivate the development of the random decomposition upper-confidence bound algorithm (RDUCB) that is straightforward to implement - (almost) plug-and-play - and, surprisingly, yields significant empirical gains compared to the previous state-of-the-art on a comprehensive set of benchmarks. We also confirm the plug-and-play nature of our modelling component by integrating our method with HEBO, showing improved practical gains in the highest dimensional tasks from Bayesmark.
Verification of discrete time or continuous time dynamical systems over the reals is known to be undecidable. It is however known that undecidability does not hold for various classes of systems: if robustness is defined as the fact that reachability relation is stable under infinitesimal perturbation, then their reachability relation is decidable. In other words, undecidability implies sensitivity under infinitesimal perturbation, a property usually not expected in systems considered in practice, and hence can be seen (somehow informally) as an artefact of the theory, that always assumes exactness. In a similar vein, it is known that, while undecidability holds for logical formulas over the reals, it does not hold when considering delta-undecidability: one must determine whether a property is true, or $\delta$-far from being true. We first extend the previous statements to a theory for general (discrete time, continuous-time, and even hybrid) dynamical systems, and we relate the two approaches. We also relate robustness to some geometric properties of reachability relation. But mainly, when a system is robust, it then makes sense to quantify at which level of perturbation. We prove that assuming robustness to polynomial perturbations on precision leads to reachability verifiable in complexity class PSPACE, and even to a characterization of this complexity class. We prove that assuming robustness to polynomial perturbations on time or length of trajectories leads to similar statements, but with PTIME. It has been recently unexpectedly shown that the length of a solution of a polynomial ordinary differential equation corresponds to a time of computation: PTIME corresponds to solutions of polynomial differential equations of polynomial length. Our results argue that the answer is given by precision: space corresponds to the involved precision.
Due to its simple installation and connectivity, the Internet of Things (IoT) is susceptible to malware attacks. Being able to operate autonomously. As IoT devices have become more prevalent, they have become the most tempting targets for malware. Weak, guessable, or hard-coded passwords, and a lack of security measures contribute to these vulnerabilities along with insecure network connections and outdated update procedures. To understand IoT malware, current methods and analysis ,using static methods, are ineffective. The field of deep learning has made great strides in recent years due to their tremendous data mining, learning, and expression capabilities, cybersecurity has enjoyed tremendous growth in recent years. As a result, malware analysts will not have to spend as much time analyzing malware. In this paper, we propose a novel detection and analysis method that harnesses the power and simplicity of decision trees. The experiments are conducted using a real word dataset, MaleVis which is a publicly available dataset. Based on the results, we show that our proposed approach outperforms existing state-of-the-art solutions in that it achieves 97.23% precision and 95.89% recall in terms of detection and classification. A specificity of 96.58%, F1-score of 96.40%, an accuracy of 96.43.
Bayesian model comparison (BMC) offers a principled approach for assessing the relative merits of competing computational models and propagating uncertainty into model selection decisions. However, BMC is often intractable for the popular class of hierarchical models due to their high-dimensional nested parameter structure. To address this intractability, we propose a deep learning method for performing BMC on any set of hierarchical models which can be instantiated as probabilistic programs. Since our method enables amortized inference, it allows efficient re-estimation of posterior model probabilities and fast performance validation prior to any real-data application. In a series of extensive validation studies, we benchmark the performance of our method against the state-of-the-art bridge sampling method and demonstrate excellent amortized inference across all BMC settings. We then use our method to compare four hierarchical evidence accumulation models that have previously been deemed intractable for BMC due to partly implicit likelihoods. In this application, we corroborate evidence for the recently proposed L\'evy flight model of decision-making and show how transfer learning can be leveraged to enhance training efficiency. Reproducible code for all analyses is provided.
This paper proposes a recommender system to alleviate the cold-start problem that can estimate user preferences based on only a small number of items. To identify a user's preference in the cold state, existing recommender systems, such as Netflix, initially provide items to a user; we call those items evidence candidates. Recommendations are then made based on the items selected by the user. Previous recommendation studies have two limitations: (1) the users who consumed a few items have poor recommendations and (2) inadequate evidence candidates are used to identify user preferences. We propose a meta-learning-based recommender system called MeLU to overcome these two limitations. From meta-learning, which can rapidly adopt new task with a few examples, MeLU can estimate new user's preferences with a few consumed items. In addition, we provide an evidence candidate selection strategy that determines distinguishing items for customized preference estimation. We validate MeLU with two benchmark datasets, and the proposed model reduces at least 5.92% mean absolute error than two comparative models on the datasets. We also conduct a user study experiment to verify the evidence selection strategy.
小貼士
登錄享
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191