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

Models with intractable normalising functions have numerous applications. Because the normalising constants are functions of the parameters of interest, standard Markov chain Monte Carlo cannot be used for Bayesian inference for these models. Many algorithms have been developed for such models. Some have the posterior distribution as the asymptotic distribution. Other ``asymptotically inexact'' algorithms do not possess this property. There is limited guidance for evaluating approximations based on these algorithms. We propose two new diagnostics that address these problems. We provide theoretical justification for our methods and apply them to several algorithms in the context of challenging examples.

Inverse problems are paramount in Science and Engineering. In this paper, we consider the setup of Statistical Inverse Problem (SIP) and demonstrate how Stochastic Gradient Descent (SGD) algorithms can be used in the linear SIP setting. We provide consistency and finite sample bounds for the excess risk. We also propose a modification for the SGD algorithm where we leverage machine learning methods to smooth the stochastic gradients and improve empirical performance. We exemplify the algorithm in a setting of great interest nowadays: the Functional Linear Regression model. In this case we consider a synthetic data example and examples with a real data classification problem.

In the present work we propose and study a time discrete scheme for the following chemotaxis-consumption model (for any $s\ge 1$), $$\partial_t u - \Delta u = - \nabla \cdot (u \nabla v), \quad \partial_t v - \Delta v = - u^s v \quad \hbox{in $(0,T)\times \Omega$,}$$ endowed with isolated boundary conditions and initial conditions, where $(u,v)$ model cell density and chemical signal concentration. The proposed scheme is defined via a reformulation of the model, using the auxiliary variable $z = \sqrt{v + \alpha^2}$ combined with a Backward Euler scheme for the $(u,z)$ problem and a upper truncation of $u$ in the nonlinear chemotaxis and consumption terms. Then, two different ways of retrieving an approximation for the function $v$ are provided. We prove the existence of solution to the time discrete scheme and establish uniform in time \emph{a priori} estimates, yielding to the convergence of the scheme towards a weak solution $(u,v)$ of the chemotaxis-consumption model.

Statistical quality control methods are noteworthy to producing standard production in manufacturing processes. In this regard, there are many classical manners to control the process. Many of them have a global assumption around the distributions of the process data. They are supposed to be Normal, but it is clear that it is not always valid for all processes. Such control charts made some wrong decisions that waste funds. So, the main question while working with multivariate data set is how to find the multivariate distribution of the data set, which saves the original dependency between variables. To our knowledge, a copula function guarantees dependence on the result function. It is not enough when there is no other fundamental information about the statistical society, and we have just a data set. Therefore, we apply the maximum entropy concept to deal with this situation. In this paper, first of all, we get the joint distribution of a data set from a manufacturing process that needs to be in-control while running the production process. Then, we get an elliptical control limit via the maximum copula entropy. Finally, we represent a practical example using the method. Average run lengths are calculated for some means and shifts to show the ability of the maximum copula entropy. In the end, two practical data examples are presented, and the results of our method are compared with the traditional way based on Fisher distribution.

Transfer learning has become an essential technique to exploit information from the source domain to boost performance of the target task. Despite the prevalence in high-dimensional data, heterogeneity and/or heavy tails tend to be discounted in current transfer learning approaches and thus may undermine the resulting performance. We propose a transfer learning procedure in the framework of high-dimensional quantile regression models to accommodate the heterogeneity and heavy tails in the source and target domains. We establish error bounds of the transfer learning estimator based on delicately selected transferable source domains, showing that lower error bounds can be achieved for critical selection criterion and larger sample size of source tasks. We further propose valid confidence interval and hypothesis test procedures for individual component of quantile regression coefficients by advocating a one-step debiased estimator of transfer learning estimator wherein the consistent variance estimation is proposed via the technique of transfer learning again. Simulation results demonstrate that the proposed method exhibits some favorable performances.

The subset sum problem is known to be an NP-hard problem in the field of computer science with the fastest known approach having a run-time complexity of $O(2^{0.3113n})$. A modified version of this problem is known as the perfect sum problem and extends the subset sum idea further. This extension results in additional complexity, making it difficult to compute for a large input. In this paper, I propose a probabilistic approach which approximates the solution to the perfect sum problem by approximating the distribution of potential sums. Since this problem is an extension of the subset sum, our approximation also grants some probabilistic insight into the solution for the subset sum problem. We harness distributional approximations to model the number of subsets which sum to a certain size. These distributional approximations are formulated in two ways: using bounds to justify normal approximation, and approximating the empirical distribution via density estimation. These approximations can be computed in $O(n)$ complexity, and can increase in accuracy with the size of the input data making it useful for large-scale combinatorial problems. Code is available at //github.com/KristofPusztai/PerfectSum.

Earlier studies have revealed that Maxwell's demon must obey the second law of thermodynamics. However, it is still an open question whether there is a fundamental net gain and indispensability of using information. Here, gain refers to free energy or mechanical work. In this paper, we report a novel generalization of the second law of thermodynamics that answers this question in affirmative. The entropy production can be split into two contributions: the entropy productions of the individual subsystems and the decrease in the correlations internally between subsystems. Our novel generalization of the second law implies that information is indispensable and that a positive net gain can be realized if an agent exploits the latter contribution of this split. Particularly, it is shown that the total entropy production has a lower bound corresponding to the positive quantity that emerges when the internal correlations of the target system diminish without the correlation between an agent and the target of its control. In other words, the target information is indispensable for exploiting the internal correlations to extract free energy or work. As the internal correlations can grow linearly with the number of the subsystems constituting the target system, the control with such correlations, i.e., feedback control, can provide substantial gain that exceeds the operational cost paid for performing the feedback control, which is negligible in the thermodynamic limit. Thus, the generalized second law presented in this paper can be interpreted as a physical principle that explains the mechanism through which information becomes not only substantially beneficial and but also inevitable at the macroscopic scale.

Gradient estimation -- approximating the gradient of an expectation with respect to the parameters of a distribution -- is central to the solution of many machine learning problems. However, when the distribution is discrete, most common gradient estimators suffer from excessive variance. To improve the quality of gradient estimation, we introduce a variance reduction technique based on Stein operators for discrete distributions. We then use this technique to build flexible control variates for the REINFORCE leave-one-out estimator. Our control variates can be adapted online to minimize variance and do not require extra evaluations of the target function. In benchmark generative modeling tasks such as training binary variational autoencoders, our gradient estimator achieves substantially lower variance than state-of-the-art estimators with the same number of function evaluations.

Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path in a large graph, neural networks allow learning from data to predict the most likely answer in more complex tasks such as image classification, which cannot be reduced to an exact algorithm. To get the best of both worlds, this thesis explores combining both concepts leading to more robust, better performing, more interpretable, more computationally efficient, and more data efficient architectures. The thesis formalizes the idea of algorithmic supervision, which allows a neural network to learn from or in conjunction with an algorithm. When integrating an algorithm into a neural architecture, it is important that the algorithm is differentiable such that the architecture can be trained end-to-end and gradients can be propagated back through the algorithm in a meaningful way. To make algorithms differentiable, this thesis proposes a general method for continuously relaxing algorithms by perturbing variables and approximating the expectation value in closed form, i.e., without sampling. In addition, this thesis proposes differentiable algorithms, such as differentiable sorting networks, differentiable renderers, and differentiable logic gate networks. Finally, this thesis presents alternative training strategies for learning with algorithms.

The conjoining of dynamical systems and deep learning has become a topic of great interest. In particular, neural differential equations (NDEs) demonstrate that neural networks and differential equation are two sides of the same coin. Traditional parameterised differential equations are a special case. Many popular neural network architectures, such as residual networks and recurrent networks, are discretisations. NDEs are suitable for tackling generative problems, dynamical systems, and time series (particularly in physics, finance, ...) and are thus of interest to both modern machine learning and traditional mathematical modelling. NDEs offer high-capacity function approximation, strong priors on model space, the ability to handle irregular data, memory efficiency, and a wealth of available theory on both sides. This doctoral thesis provides an in-depth survey of the field. Topics include: neural ordinary differential equations (e.g. for hybrid neural/mechanistic modelling of physical systems); neural controlled differential equations (e.g. for learning functions of irregular time series); and neural stochastic differential equations (e.g. to produce generative models capable of representing complex stochastic dynamics, or sampling from complex high-dimensional distributions). Further topics include: numerical methods for NDEs (e.g. reversible differential equations solvers, backpropagation through differential equations, Brownian reconstruction); symbolic regression for dynamical systems (e.g. via regularised evolution); and deep implicit models (e.g. deep equilibrium models, differentiable optimisation). We anticipate this thesis will be of interest to anyone interested in the marriage of deep learning with dynamical systems, and hope it will provide a useful reference for the current state of the art.