For many Markov chains that arise in applications (health, finance, etc.), state spaces are huge, and existing matrix methods may not be practical or even not possible to implement. In the literature, the expected wai...
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ISBN:
(数字)9798350376968
ISBN:
(纸本)9798350376975
For many Markov chains that arise in applications (health, finance, etc.), state spaces are huge, and existing matrix methods may not be practical or even not possible to implement. In the literature, the expected waiting time for Markov chain (with a smaller number of states) generated patterns are obtained by finding an appropriate pattern matrix and solving a set of linear equations. In this paper, a fuzzy transition probability (TP) matrix is introduced, and a data-driven fuzzy pattern mining algorithm is proposed for sequence data of any length. The proposed algorithm, which avoids the inversion of the pattern matrix, is applicable to Markov chains with huge state spaces. The proposed algorithm studies two examples involving DNA sequence data with 3954 base pairs and patterns generated by the log-returns of the stocks/cryptocurrencies. Expected weighting times are compared with the traditional matrix approach. Incorporating stochastic variation in the TP estimates through fuzzy matrices, the new approach provides an alternative path to produce
$\alpha$
-cuts for TP matrices. The main contribution of this paper is to fit an appropriate MC model to a given sequence data and use the proposed fuzzy pattern mining algorithm to obtain resilient probabilistic forecasts and expected waiting time to reach patterns of interest.
We show that the Fourier transform of Patterson-Sullivan measures associated to convex cocompact groups of isometries of real hyperbolic space decays polynomially quickly at infinity. The proof is based on the L2-flat...
Automatic differentiation variational inference (ADVI) offers fast and easy-to-use posterior approximation in multiple modern probabilistic programming languages. However, its stochastic optimizer lacks clear converge...
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Automatic differentiation variational inference (ADVI) offers fast and easy-to-use posterior approximation in multiple modern probabilistic programming languages. However, its stochastic optimizer lacks clear convergence criteria and requires tuning parameters. Moreover, ADVI inherits the poor posterior uncertainty estimates of mean-field variational Bayes (MFVB). We introduce "deterministic ADVI" (DADVI) to address these issues. DADVI replaces the intractable MFVB objective with a fixed Monte Carlo approximation, a technique known in the stochastic optimization literature as the "sample average approximation" (SAA). By optimizing an approximate but deterministic objective, DADVI can use off-the-shelf second-order optimization, and, unlike standard mean-field ADVI, is amenable to more accurate posterior covariances via linear response (LR). In contrast to existing worst-case theory, we show that, on certain classes of common statistical problems, DADVI and the SAA can perform well with relatively few samples even in very high dimensions, though we also show that such favorable results cannot extend to variational approximations that are too expressive relative to mean-field ADVI. We show on a variety of real-world problems that DADVI reliably finds good solutions with default settings (unlike ADVI) and, together with LR covariances, is typically faster and more accurate than standard ADVI.
We study transfer learning for estimation in latent variable network models. In our setting, the conditional edge probability matrices given the latent variables are represented by P for the source and Q for the targe...
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We take the first step in studying general sequential decision-making under two adaptivity constraints: rare policy switch and batch learning. First, we provide a general class called the Eluder Condition class, which...
We take the first step in studying general sequential decision-making under two adaptivity constraints: rare policy switch and batch learning. First, we provide a general class called the Eluder Condition class, which includes a wide range of reinforcement learning classes. Then, for the rare policy switch constraint, we provide a generic algorithm to achieve a Õ(log K) switching cost with a Õ(log √K) regret on the EC class. For the batch learning constraint, we provide an algorithm that provides a Õ(√K + K/B) regret with the number of batches B. This paper is the first work considering rare policy switch and batch learning under general function classes, which covers nearly all the models studied in the previous works such as tabular MDP (Bai et al., 2019; Zhang et al., 2020), linear MDP (Wang et al., 2021; Gao et al., 2021), low eluder dimension MDP (Kong et al., 2021; Velegkas et al., 2022), generalized linear function approximation (Qiao et al., 2023), and also some new classes such as the low DΔ-type Bellman eluder dimension problem, linear mixture MDP, kernelized nonlinear regulator and undercomplete partially observed Markov decision process (POMDP).
We establish precise structural and risk equivalences between subsampling and ridge regularization for ensemble ridge estimators. Specifically, we prove that linear and quadratic functionals of subsample ridge estimat...
We establish precise structural and risk equivalences between subsampling and ridge regularization for ensemble ridge estimators. Specifically, we prove that linear and quadratic functionals of subsample ridge estimators, when fitted with different ridge regularization levels λ and subsample aspect ratios ψ, are asymptotically equivalent along specific paths in the (λ, ψ)-plane (where ψ is the ratio of the feature dimension to the subsample size). Our results only require bounded moment assumptions on feature and response distributions and allow for arbitrary joint distributions. Furthermore, we provide a data-dependent method to determine the equivalent paths of (λ, ψ). An indirect implication of our equivalences is that optimally tuned ridge regression exhibits a monotonic prediction risk in the data aspect ratio. This resolves a recent open problem raised by Nakkiran et al. [1] for general data distributions under proportional asymptotics, assuming a mild regularity condition that maintains regression hardness through linearized signal-to-noise ratios.
The multi-view Gaussian process latent variable model (MV-GPLVM) aims to learn a unified representation from multi-view data but is hindered by challenges such as limited kernel expressiveness and low computational ef...
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In this paper we deal with production situations where a cap or limit to the amount of greenhouse gas emissions permitted is imposed. Fixing a tax for each ton of pollutant emitted is also considered. We use bankruptc...
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In recent years, researchers and health care professionals have been interested in medical image fusion, which combines images of the human body, organs, and cells with general information to address medical difficult...
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In this paper, the problem of resource allocation for non-orthogonal multiple access (NOMA) enabled secure federated learning (FL) is investigated. In the considered model, a set of users participate in the FL trainin...
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