The reconstruction from observations of high-dimensional chaotic dynamics such as geophysical flows is hampered by (i) the partial and noisy observations that can realistically be obtained, (ii) the need to learn from long time series of data, and (iii) the unstable nature of the dynamics. To achieve such inference from the observations over long time series, it has been suggested to combine data assimilation and machine learning in several ways. We show how to unify these approaches from a Bayesian perspective using expectation-maximization and coordinate descents. Implementations and approximations of these methods are also discussed. Finally, we numerically and successfully test the approach on two relevant low-order chaotic models with distinct identifiability.

Distributed statistical inference has recently attracted immense attention. Herein, we study the asymptotic efficiency of the maximum likelihood estimator (MLE), the one-step MLE, and the aggregated estimating equation estimator for generalized linear models with a diverging number of covariates. Then a novel method is proposed to obtain an asymptotically efficient estimator for large-scale distributed data by two rounds of communication between local machines and the central server. The assumption on the number of machines in this paper is more relaxed and thus practical for real-world applications. Simulations and a case study demonstrate the satisfactory finite-sample performance of the proposed estimators. Keywords: Generalized linear models, Large-scale distributed data, Asymptotic efficiency, One-step MLE, Diverging p MSC: 62J12 1 . Introduction In modern times, large-scale data sets have become increasingly common, and they are often stored across multiple machines. Since communication cost between machines is considerably higher than the cost of conducting statistical analysis on a single machine (Jaggi et al., 2014; Smith et al., 2018), it is inefficient to calculate a global estimator by the transmission of the local data to a central machine. Further, the application of the traditional iterative algorithms in a distributed system, such as the Fisher-scoring algorithm for maximum likelihood estimator (MLE) in generalized linear models (GLMs), cannot avoid multiple rounds of communication that incurs exorbitant costs. Therefore, communication-efficient distributed algorithms must be developed to accommodate the new features of modern data sets.

After long arguments between positivism and falsificationism, the verification of universal hypotheses was replaced with the confirmation of uncertain major premises. Unfortunately, Hemple discovered the Raven Paradox (RP). Then, Carnap used the logical probability increment as the confirmation measure. So far, many confirmation measures have been proposed. Measure F among them proposed by Kemeny and Oppenheim possesses symmetries and asymmetries proposed by Elles and Fitelson, monotonicity proposed by Greco et al., and normalizing property suggested by many researchers. Based on the semantic information theory, a measure b* similar to F is derived from the medical test. Like the likelihood ratio, b* and F can only indicate the quality of channels or the testing means instead of the quality of probability predictions. And, it is still not easy to use b*, F, or another measure to clarify the RP. For this reason, measure c* similar to the correct rate is derived. The c* has the simple form: (a-c)/max(a, c); it supports the Nicod Criterion and undermines the Equivalence Condition, and hence, can be used to eliminate the RP. Some examples are provided to show why it is difficult to use one of popular confirmation measures to eliminate the RP. Measure F, b*, and c* indicate that fewer counterexamples' existence is more essential than more positive examples' existence, and hence, are compatible with Popper's falsification thought.

Feature selection is important for modeling high-dimensional data, where the number of variables can be much larger than the sample size. In this paper, we develop a support detection and root finding procedure to learn the high dimensional sparse generalized linear models and denote this method by GSDAR. Based on the KKT condition for $\ell_0$-penalized maximum likelihood estimations, GSDAR generates a sequence of estimators iteratively. Under some restricted invertibility conditions on the maximum likelihood function and sparsity assumption on the target coefficients, the errors of the proposed estimate decays exponentially to the optimal order. Moreover, the oracle estimator can be recovered if the target signal is stronger than the detectable level. We conduct simulations and real data analysis to illustrate the advantages of our proposed method over several existing methods, including Lasso and MCP.

The examples are considered to be of the form ( x i,y i), where x i is the feature vector of the i-th example and y i { 1, 1} is its class label. Extension to the multiclass case is often handled by breaking down the problem into multiple binary ones, so our analysis and its main results can carry over to the multiclass case. We consider the online setting where examples are presented to the learner in M minibatches 2 of size b. On the n -th iteration the learner performs the following steps: 1. Receive new examples x i, x i minibatch n 2. Predict the label ˆ y i and/or the probability estimate ˆ p(y i 1 x i), i minibatch n 3. Get true labels y i f ( x i), x i minibatch n, where f is the labelling function 4. Update learner parameters accordingly The steps above are intentionally left general enough to describe all learning components encountered in the paper. Our goal is to study the quality of the probability estimates generated by online boosting ensembles and strategies for improving it. Online boosting ensembles consist of multiple base learners, themselves also trained in an online fashion and -as we will seethe techniques used for improving the probability estimates (both the calibrator and the reward models of the bandits) are also learners trained in an online fashion. All follow the same general approach defined above: they maintain a model with a fixed number of parameters (i.e.

Algorithmic fairness involves expressing notions such as equity, or reasonable treatment, as quantifiable measures that a machine learning algorithm can optimise. Most work in the literature to date has focused on classification problems where the prediction is categorical, such as accepting or rejecting a loan application. This is in part because classification fairness measures are easily computed by comparing the rates of outcomes, leading to behaviours such as ensuring that the same fraction of eligible men are selected as eligible women. But such measures are computationally difficult to generalise to the continuous regression setting for problems such as pricing, or allocating payments. The difficulty arises from estimating conditional densities (such as the probability density that a system will over-charge by a certain amount). For the regression setting we introduce tractable approximations of the independence, separation and sufficiency criteria by observing that they factorise as ratios of different conditional probabilities of the protected attributes. We introduce and train machine learning classifiers, distinct from the predictor, as a mechanism to estimate these probabilities from the data. This naturally leads to model agnostic, tractable approximations of the criteria, which we explore experimentally.

The chart of the nuclides is limited by particle drip lines beyond which nuclear stability to proton or neutron emission is lost. Predicting the range of particle-bound isotopes poses an appreciable challenge for nuclear theory as it involves extreme extrapolations of nuclear masses beyond the regions where experimental information is available. Still, quantified extrapolations are crucial for a variety of applications, including the modeling of stellar nucleosynthesis. We use microscopic nuclear mass models and Bayesian methodology to provide quantified predictions of proton and neutron separation energies as well as Bayesian probabilities of existence throughout the nuclear landscape all the way to the particle drip lines. We apply nuclear density functional theory with several energy density functionals. To account for uncertainties, Bayesian Gaussian processes are trained on the separation-energy residuals for each individual model, and the resulting predictions are combined via Bayesian model averaging. This framework allows to account for systematic and statistical uncertainties and propagate them to extrapolative predictions. We characterize the drip-line regions where the probability that the nucleus is particle-bound decreases from $1$ to $0$. In these regions, we provide quantified predictions for one- and two-nucleon separation energies. According to our Bayesian model averaging analysis, 7759 nuclei with $Z\leq 119$ have a probability of existence $\geq 0.5$. The extrapolations obtained in this study will be put through stringent tests when new experimental information on exotic nuclei becomes available. In this respect, the quantified landscape of nuclear existence obtained in this study should be viewed as a dynamical prediction that will be fine-tuned when new experimental information and improved global mass models become available.

We consider the effect of structure-agnostic and structure-dependent masking schemes when training a universal marginaliser (arXiv:1711.00695) in order to learn conditional distributions of the form $P(x_i |\mathbf x_{\mathbf b})$, where $x_i$ is a given random variable and $\mathbf x_{\mathbf b}$ is some arbitrary subset of all random variables of the generative model of interest. In other words, we mimic the self-supervised training of a denoising autoencoder, where a dataset of unlabelled data is used as partially observed input and the neural approximator is optimised to minimise reconstruction loss. We focus on studying the underlying process of the partially observed data---how good is the neural approximator at learning all conditional distributions when the observation process at prediction time differs from the masking process during training? We compare networks trained with different masking schemes in terms of their predictive performance and generalisation properties.

In many scenarios, humans prefer a text-based representation of quantitative data over numerical, tabular, or graphical representations. The attractiveness of textual summaries for complex data has inspired research on data-to-text systems. While there are several data-to-text tools for time series, few of them try to mimic how humans summarize for time series. In this paper, we propose a model to create human-like text descriptions for time series. Our system finds patterns in time series data and ranks these patterns based on empirical observations of human behavior using utility estimation. Our proposed utility estimation model is a Bayesian network capturing interdependencies between different patterns. We describe the learning steps for this network and introduce baselines along with their performance for each step. The output of our system is a natural language description of time series that attempts to match a human's summary of the same data.

In recent years, Markov logic networks (MLNs) have been proposed as a potentially useful paradigm for music signal analysis. Because all hidden Markov models can be reformulated as MLNs, the latter can provide an all-encompassing framework that reuses and extends previous work in the field. However, just because it is theoretically possible to reformulate previous work as MLNs, does not mean that it is advantageous. In this paper, we analyse some proposed examples of MLNs for musical analysis and consider their practical disadvantages when compared to formulating the same musical dependence relationships as (dynamic) Bayesian networks. We argue that a number of practical hurdles such as the lack of support for sequences and for arbitrary continuous probability distributions make MLNs less than ideal for the proposed musical applications, both in terms of easy of formulation and computational requirements due to their required inference algorithms. These conclusions are not specific to music, but apply to other fields as well, especially when sequential data with continuous observations is involved. Finally, we show that the ideas underlying the proposed examples can be expressed perfectly well in the more commonly used framework of (dynamic) Bayesian networks.