The focus of the present paper is to investigate the following questions: to what extent syntactic features capture phylogenetic relationships and to what extent Markov models are a viable assumption for phylogenetic reconstruction based on syntactic features. For the second, we also consider an alternative that we argue approximates the infinite site evolutionary model. These questions are motivated by the fact that at both lexical and syntactic level, Markov processes are commonly assumed to underlie computational models of language change; for instance, within the Principles and Parameters setting relevant here, Niyogi and Berwick (1997) developed models of language acquisition and language change based on a Markov process in a space of syntactic parameters. In this paper we focus only on language change processes, viewed through the lens of phylogenetic trees of language families. While the model we consider are not directly related to models of language acquisition and parameter setting, the historical changes of syntax within and across language families, through the modification of syntactic parameters, can be seen as an effect of such underlying dynamics.

We study policy optimization for Markov decision processes (MDPs) with multiple reward value functions, which are to be jointly optimized according to given criteria such as proportional fairness (smooth concave scalarization), hard constraints (constrained MDP), and max-min trade-off. We propose an Anchor-changing Regularized Natural Policy Gradient (ARNPG) framework, which can systematically incorporate ideas from well-performing first-order methods into the design of policy optimization algorithms for multi-objective MDP problems. Theoretically, the designed algorithms based on the ARNPG framework achieve $\tilde{O}(1/T)$ global convergence with exact gradients. Empirically, the ARNPG-guided algorithms also demonstrate superior performance compared to some existing policy gradient-based approaches in both exact gradients and sample-based scenarios.

The goal of this thesis is to develop the optimisation and generalisation theoretic foundations of learning in artificial neural networks. On optimisation, a new theoretical framework is proposed for deriving architecture-dependent first-order optimisation algorithms. The approach works by combining a "functional majorisation" of the loss function with "architectural perturbation bounds" that encode an explicit dependence on neural architecture. The framework yields optimisation methods that transfer hyperparameters across learning problems. On generalisation, a new correspondence is proposed between ensembles of networks and individual networks. It is argued that, as network width and normalised margin are taken large, the space of networks that interpolate a particular training set concentrates on an aggregated Bayesian method known as a "Bayes point machine". This correspondence provides a route for transferring PAC-Bayesian generalisation theorems over to individual networks. More broadly, the correspondence presents a fresh perspective on the role of regularisation in networks with vastly more parameters than data.

Extreme multi-label classification (XMC), or extreme multi-label learning, aims to find the relevant labels for a data input from an enormous label space. With increasingly growing information in the era of big data, XMC has become more and more important, and has been widely applied to various real-world applications, such as advertising [37], product search [9], and document retrieval [6]. However, for domains with potential high risks from mistakes like public health and medicine, it is crucial to model the predictive uncertainty for their downstream XMC applications like food classification [54] and medical diagnosis [2]. In particular, an input sometimes could have only few or even no matches in the label space, so the outputs could be noisy without uncertainty quantification. It is also insufficient to only model uncertainty for the entire input since XMC models could have different confidence for each label among the whole enormous space. To estimate predictive uncertainty, Bayesian and probabilistic models [20] are inherently applicable because variance can intrinsically be viewed as an uncertainty measurement. However, although Bayesian approaches are mathematically grounded to model uncertainty, their computational costs are usually exorbitant for large-scale data. To address this issue, the most popular solution is to approximate Bayesian inference by sampling models as an ensemble [17].

In this article, we have seen the Bayesian approach in action with the help of a small example. It uses prior knowledge and updates it with observed data to create a posterior, exactly like humans intuitively do. This approach is better than discarding the data and just proceeding with some prior, obviously. It is even more powerful than the maximum likelihood method: you can see this by choosing a flat prior, i.e. the prior gives the same probability (or density) to every possible value θ and is essentially a constant. Furthermore, the Bayes method even gives you a distribution of the parameters, while the maximum likelihood method does not.

Parameter estimation and associated uncertainty quantification is an important problem in dynamical systems characterized by ordinary differential equation (ODE) models that are often nonlinear. Typically, such models have analytically intractable trajectories which result in likelihoods and posterior distributions that are similarly intractable. Bayesian inference for ODE systems via simulation methods require numerical approximations to produce inference with high accuracy at a cost of heavy computational power and slow convergence. At the same time, Artificial Neural Networks (ANN) offer tractability that can be utilized to construct an approximate but tractable likelihood and posterior distribution. In this paper we propose a hybrid approach, where Laplace-based Bayesian inference is combined with an ANN architecture for obtaining approximations to the ODE trajectories as a function of the unknown initial values and system parameters. Suitable choices of a collocation grid and customized loss functions are proposed to fine tune the ODE trajectories and Laplace approximation. The effectiveness of our proposed methods is demonstrated using an epidemiological system with non-analytical solutions, the Susceptible-Infectious-Removed (SIR) model for infectious diseases, based on simulated and real-life influenza datasets. The novelty and attractiveness of our proposed approach include (i) a new development of Bayesian inference using ANN architectures for ODE based dynamical systems, and (ii) a computationally fast posterior inference by avoiding convergence issues of benchmark Markov Chain Monte Carlo methods. These two features establish the developed approach as an accurate alternative to traditional Bayesian computational methods, with improved computational cost.

Markov Chain Monte Carlo (MCMC) algorithms do not scale well for large datasets leading to difficulties in Neural Network posterior sampling. In this paper, we apply a generalization of the Metropolis Hastings algorithm that allows us to restrict the evaluation of the likelihood to small mini-batches in a Bayesian inference context. Since it requires the computation of a so-called "noise penalty" determined by the variance of the training loss function over the mini-batches, we refer to this data subsampling strategy as Penalty Bayesian Neural Networks - PBNNs. Its implementation on top of MCMC is straightforward, as the variance of the loss function merely reduces the acceptance probability. Comparing to other samplers, we empirically show that PBNN achieves good predictive performance for a given mini-batch size. Varying the size of the mini-batches enables a natural calibration of the predictive distribution and provides an inbuilt protection against overfitting. We expect PBNN to be particularly suited for cases when data sets are distributed across multiple decentralized devices as typical in federated learning.

Recent advances on large-scale pre-training have shown great potentials of leveraging a large set of Pre-Trained Models (PTMs) for improving Out-of-Distribution (OoD) generalization, for which the goal is to perform well on possible unseen domains after fine-tuning on multiple training domains. However, maximally exploiting a zoo of PTMs is challenging since fine-tuning all possible combinations of PTMs is computationally prohibitive while accurate selection of PTMs requires tackling the possible data distribution shift for OoD tasks. In this work, we propose ZooD, a paradigm for PTMs ranking and ensemble with feature selection. Our proposed metric ranks PTMs by quantifying inter-class discriminability and inter-domain stability of the features extracted by the PTMs in a leave-one-domain-out cross-validation manner. The top-K ranked models are then aggregated for the target OoD task. To avoid accumulating noise induced by model ensemble, we propose an efficient variational EM algorithm to select informative features. We evaluate our paradigm on a diverse model zoo consisting of 35 models for various OoD tasks and demonstrate: (i) model ranking is better correlated with fine-tuning ranking than previous methods and up to 9859x faster than brute-force fine-tuning; (ii) OoD generalization after model ensemble with feature selection outperforms the state-of-the-art methods and the accuracy on most challenging task DomainNet is improved from 46.5\% to 50.6\%. Furthermore, we provide the fine-tuning results of 35 PTMs on 7 OoD datasets, hoping to help the research of model zoo and OoD generalization. Code will be available at https://gitee.com/mindspore/models/tree/master/research/cv/zood.

Maximum mutual information (MMI) has become one of the two de facto methods for sequence-level training of speech recognition acoustic models. This paper aims to isolate, identify and bring forward the implicit modelling decisions induced by the design implementation of standard finite state transducer (FST) lattice based MMI training framework. The paper particularly investigates the necessity to maintain a preselected numerator alignment and raises the importance of determinizing FST denominator lattices on the fly. The efficacy of employing on the fly FST lattice determinization is mathematically shown to guarantee discrimination at the hypothesis level and is empirically shown through training deep CNN models on a 18K hours Mandarin dataset and on a 2.8K hours English dataset. On assistant and dictation tasks, the approach achieves between 2.3-4.6% relative WER reduction (WERR) over the standard FST lattice based approach.

Although evaluation of the expectations on the Ising model is essential in various applications, it is mostly infeasible because of intractable multiple summations. Spatial Monte Carlo integration (SMCI) is a sampling-based approximation. It can provide high-accuracy estimations for such intractable expectations. To evaluate the expectation of a function of variables in a specific region (called target region), SMCI considers a larger region containing the target region (called sum region). In SMCI, the multiple summation for the variables in the sum region is precisely executed, and that in the outer region is evaluated by the sampling approximation such as the standard Monte Carlo integration. It is guaranteed that the accuracy of the SMCI estimator improves monotonically as the size of the sum region increases. However, a haphazard expansion of the sum region could cause a combinatorial explosion. Therefore, we hope to improve the accuracy without such an expansion. In this paper, based on the theory of generalized least squares (GLS), a new effective method is proposed by combining multiple SMCI estimators. The validity of the proposed method is demonstrated theoretically and numerically. The results indicate that the proposed method can be effective in the inverse Ising problem (or Boltzmann machine learning).