亚洲男人的天堂2018av,欧美草比,久久久久久免费视频精选,国色天香在线看免费,久久久久亚洲av成人片仓井空

State-of-the-art methods for Bayesian inference in state-space models are (a) conditional sequential Monte Carlo (CSMC) algorithms; (b) sophisticated 'classical' MCMC algorithms like MALA, or mGRAD from Titsias and Papaspiliopoulos (2018, arXiv:1610.09641v3 [stat.ML]). The former propose $N$ particles at each time step to exploit the model's 'decorrelation-over-time' property and thus scale favourably with the time horizon, $T$ , but break down if the dimension of the latent states, $D$, is large. The latter leverage gradient-/prior-informed local proposals to scale favourably with $D$ but exhibit sub-optimal scalability with $T$ due to a lack of model-structure exploitation. We introduce methods which combine the strengths of both approaches. The first, Particle-MALA, spreads $N$ particles locally around the current state using gradient information, thus extending MALA to $T > 1$ time steps and $N > 1$ proposals. The second, Particle-mGRAD, additionally incorporates (conditionally) Gaussian prior dynamics into the proposal, thus extending the mGRAD algorithm to $T > 1$ time steps and $N > 1$ proposals. We prove that Particle-mGRAD interpolates between CSMC and Particle-MALA, resolving the 'tuning problem' of choosing between CSMC (superior for highly informative prior dynamics) and Particle-MALA (superior for weakly informative prior dynamics). We similarly extend other 'classical' MCMC approaches like auxiliary MALA, aGRAD, and preconditioned Crank-Nicolson-Langevin (PCNL) to $T > 1$ time steps and $N > 1$ proposals. In experiments, for both highly and weakly informative prior dynamics, our methods substantially improve upon both CSMC and sophisticated 'classical' MCMC approaches.

In arXiv:2305.03945 [math.NA], a first-order optimization algorithm has been introduced to solve time-implicit schemes of reaction-diffusion equations. In this research, we conduct theoretical studies on this first-order algorithm equipped with a quadratic regularization term. We provide sufficient conditions under which the proposed algorithm and its time-continuous limit converge exponentially fast to a desired time-implicit numerical solution. We show both theoretically and numerically that the convergence rate is independent of the grid size, which makes our method suitable for large-scale problems. The efficiency of our algorithm has been verified via a series of numerical examples conducted on various types of reaction-diffusion equations. The choice of optimal hyperparameters as well as comparisons with some classical root-finding algorithms are also discussed in the numerical section.

We propose a novel algorithm for the support estimation of partially known Gaussian graphical models that incorporates prior information about the underlying graph. In contrast to classical approaches that provide a point estimate based on a maximum likelihood or a maximum a posteriori criterion using (simple) priors on the precision matrix, we consider a prior on the graph and rely on annealed Langevin diffusion to generate samples from the posterior distribution. Since the Langevin sampler requires access to the score function of the underlying graph prior, we use graph neural networks to effectively estimate the score from a graph dataset (either available beforehand or generated from a known distribution). Numerical experiments demonstrate the benefits of our approach.

We present new convergence estimates of generalized empirical interpolation methods in terms of the entropy numbers of the parametrized function class. Our analysis is transparent and leads to sharper convergence rates than the classical analysis via the Kolmogorov n-width. In addition, we also derive novel entropy-based convergence estimates of the Chebyshev greedy algorithm for sparse n-term nonlinear approximation of a target function. This also improves classical convergence analysis when corresponding entropy numbers decay fast enough.

Asymptotic analysis for related inference problems often involves similar steps and proofs. These intermediate results could be shared across problems if each of them is made self-contained and easily identified. However, asymptotic analysis using Taylor expansions is limited for result borrowing because it is a step-to-step procedural approach. This article introduces EEsy, a modular system for estimating finite and infinitely dimensional parameters in related inference problems. It is based on the infinite-dimensional Z-estimation theorem, Donsker and Glivenko-Cantelli preservation theorems, and weight calibration techniques. This article identifies the systematic nature of these tools and consolidates them into one system containing several modules, which can be built, shared, and extended in a modular manner. This change to the structure of method development allows related methods to be developed in parallel and complex problems to be solved collaboratively, expediting the development of new analytical methods. This article considers four related inference problems -- estimating parameters with random sampling, two-phase sampling, auxiliary information incorporation, and model misspecification. We illustrate this modular approach by systematically developing 9 parameter estimators and 18 variance estimators for the four related inference problems regarding semi-parametric additive hazards models. Simulation studies show the obtained asymptotic results for these 27 estimators are valid. In the end, I describe how this system can simplify the use of empirical process theory, a powerful but challenging tool to be adopted by the broad community of methods developers. I discuss challenges and the extension of this system to other inference problems.

We present a novel combination of dynamic embedded topic models and change-point detection to explore diachronic change of lexical semantic modality in classical and early Christian Latin. We demonstrate several methods for finding and characterizing patterns in the output, and relating them to traditional scholarship in Comparative Literature and Classics. This simple approach to unsupervised models of semantic change can be applied to any suitable corpus, and we conclude with future directions and refinements aiming to allow noisier, less-curated materials to meet that threshold.

The celebrated Kleene fixed point theorem is crucial in the mathematical modelling of recursive specifications in Denotational Semantics. In this paper we discuss whether the hypothesis of the aforementioned result can be weakened. An affirmative answer to the aforesaid inquiry is provided so that a characterization of those properties that a self-mapping must satisfy in order to guarantee that its set of fixed points is non-empty when no notion of completeness are assumed to be satisfied by the partially ordered set. Moreover, the case in which the partially ordered set is coming from a quasi-metric space is treated in depth. Finally, an application of the exposed theory is obtained. Concretely, a mathematical method to discuss the asymptotic complexity of those algorithms whose running time of computing fulfills a recurrence equation is presented. Moreover, the aforesaid method retrieves the fixed point based methods that appear in the literature for asymptotic complexity analysis of algorithms. However, our new method improves the aforesaid methods because it imposes fewer requirements than those that have been assumed in the literature and, in addition, it allows to state simultaneously upper and lower asymptotic bounds for the running time computing.

In this paper, we provide conditions that hulls of generalized Reed-Solomon (GRS) codes are also GRS codes from algebraic geometry codes. If the conditions are not satisfied, we provide a method of linear algebra to find the bases of hulls of GRS codes and give formulas to compute their dimensions. Besides, we explain that the conditions are too good to be improved by some examples. Moreover, we show self-orthogonal and self-dual GRS codes.

We state and give self contained proofs of semidefinite programming characterizations of the numerical radius and its dual norm for matrices. We show that the computation of the numerical radius and its dual norm within $\varepsilon$ precision are polynomially time computable in the data and $|\log \varepsilon |$ using either the ellipsoid method or the short step, primal interior point method. We apply our results to give a simple formula for the spectral and nuclear norm of $2\times n\times m$ real tensor in terms of the numerical radius and its dual norm.

We derive information-theoretic generalization bounds for supervised learning algorithms based on the information contained in predictions rather than in the output of the training algorithm. These bounds improve over the existing information-theoretic bounds, are applicable to a wider range of algorithms, and solve two key challenges: (a) they give meaningful results for deterministic algorithms and (b) they are significantly easier to estimate. We show experimentally that the proposed bounds closely follow the generalization gap in practical scenarios for deep learning.