In the previous article, we studied Artificial Intelligence, its functions, and its python implementations. In this article, we will be studying Machine Learning. One thing that I believe is that if we are able to correlate anything with us or our life, there are greater chances of understanding the concept. So I will try to explain everything by relating it to humans.

Program: Monday Session I Maximilian Kasy, "Adaptive treatment assignment in experiments for policy choice" Bezirgen Veliyev, "Functional Sequential Treatment Allocation" Keynote Uri Shalit about "Machine learning and causal inference: a two-way road": "This talk will have two parts. In the first we will discuss a framework we developed for learning individualized treatment recommendations from observational health data, merging ideas from machine learning and causal inference. We will see examples of our framework applied to two crucial health problems using data from tens of thousands of patients, and discuss some important causal-inference challenges that come to focus in this setting. In the second part we will show how we use ideas from the causal inference literature to address long standing problems in machine learning: off-policy evaluation in a partially observable Markov decision process (POMDP), and learning predictive models that are stable against distributional shifts." Heterogeneous effects of training programmes for unemployed in Belgium" Daniel Jacob, "Does Tenure make you love your Job?" Nicolaj Mühlbach, "Heterogeneous Treatment Effects of an Early Retirement Reform" Tuesday Session III Dmitry Arkhangelsky, "Double-Robust Identification for Causal Panel Data Models" Martin Spindler, "Uniform Inference in High-Dimensional Gaussian Graphical Models" Keynote Stefan Wager about "Designing Loss Functions for Causal Machine Learning": "Given advances in machine learning over the past decades, it is now possible to accurately solve difficult non-parametric prediction problems in a way that is routine and reproducible.

Normalizing flows transform a simple base distribution into a complex target distribution and have proved to be powerful models for data generation and density estimation. In this work, we propose a novel type of normalizing flow driven by a differential deformation of the continuous-time Wiener process. As a result, we obtain a rich time series model whose observable process inherits many of the appealing properties of its base process, such as efficient computation of likelihoods and marginals. Furthermore, our continuous treatment provides a natural framework for irregular time series with an independent arrival process, including straightforward interpolation. We illustrate the desirable properties of the proposed model on popular stochastic processes and demonstrate its superior flexibility to variational RNN and latent ODE baselines in a series of experiments on synthetic and real-world data.

Accurate predictions of reactive mixing are critical for many Earth and environmental science problems. To investigate mixing dynamics over time under different scenarios, a high-fidelity, finite-element-based numerical model is built to solve the fast, irreversible bimolecular reaction-diffusion equations to simulate a range of reactive-mixing scenarios. A total of 2,315 simulations are performed using different sets of model input parameters comprising various spatial scales of vortex structures in the velocity field, time-scales associated with velocity oscillations, the perturbation parameter for the vortex-based velocity, anisotropic dispersion contrast, and molecular diffusion. Outputs comprise concentration profiles of the reactants and products. The inputs and outputs of these simulations are concatenated into feature and label matrices, respectively, to train 20 different machine learning (ML) emulators to approximate system behavior. The 20 ML emulators based on linear methods, Bayesian methods, ensemble learning methods, and multilayer perceptron (MLP), are compared to assess these models. The ML emulators are specifically trained to classify the state of mixing and predict three quantities of interest (QoIs) characterizing species production, decay, and degree of mixing. Linear classifiers and regressors fail to reproduce the QoIs; however, ensemble methods (classifiers and regressors) and the MLP accurately classify the state of reactive mixing and the QoIs. Among ensemble methods, random forest and decision-tree-based AdaBoost faithfully predict the QoIs. At run time, trained ML emulators are $\approx10^5$ times faster than the high-fidelity numerical simulations. Speed and accuracy of the ensemble and MLP models facilitate uncertainty quantification, which usually requires 1,000s of model run, to estimate the uncertainty bounds on the QoIs.

Encoding domain knowledge into the prior over the high-dimensional weight space is challenging in Bayesian neural networks. Two types of domain knowledge are commonly available in scientific applications: 1. feature sparsity (number of relevant features); 2. signal-to-noise ratio, quantified, for instance, as the proportion of variance explained (PVE). We show both types of domain knowledge can be encoded into the widely used Gaussian scale mixture priors with Automatic Relevance Determination. Specifically, we propose a new joint prior over the local (i.e., feature-specific) scale parameters to encode the knowledge about feature sparsity, and an algorithm to determine the global scale parameter (shared by all features) according to the PVE. Empirically, we show that the proposed informative prior improves prediction accuracy on publicly available datasets and in a genetics application.

Parameter estimation, statistical tests and confidence sets are the cornerstones of classical statistics that allow scientists to make inferences about the underlying process that generated the observed data. A key question is whether one can still construct hypothesis tests and confidence sets with proper coverage and high power in a so-called likelihood-free inference (LFI) setting; that is, a setting where the likelihood is not explicitly known but one can forward-simulate observable data according to a stochastic model. In this paper, we present $\texttt{ACORE}$ (Approximate Computation via Odds Ratio Estimation), a frequentist approach to LFI that first formulates the classical likelihood ratio test (LRT) as a parametrized classification problem, and then uses the equivalence of tests and confidence sets to build confidence regions for parameters of interest. We also present a goodness-of-fit procedure for checking whether the constructed tests and confidence regions are valid. $\texttt{ACORE}$ is based on the key observation that the LRT statistic, the rejection probability of the test, and the coverage of the confidence set are conditional distribution functions which often vary smoothly as a function of the parameters of interest. Hence, instead of relying solely on samples simulated at fixed parameter settings (as is the convention in standard Monte Carlo solutions), one can leverage machine learning tools and data simulated in the neighborhood of a parameter to improve estimates of quantities of interest. We demonstrate the efficacy of $\texttt{ACORE}$ with both theoretical and empirical results. Our implementation is available on Github.

The Dirichlet Belief Network~(DirBN) has been recently proposed as a promising approach in learning interpretable deep latent representations for objects. In this work, we leverage its interpretable modelling architecture and propose a deep dynamic probabilistic framework -- the Recurrent Dirichlet Belief Network~(Recurrent-DBN) -- to study interpretable hidden structures from dynamic relational data. The proposed Recurrent-DBN has the following merits: (1) it infers interpretable and organised hierarchical latent structures for objects within and across time steps; (2) it enables recurrent long-term temporal dependence modelling, which outperforms the one-order Markov descriptions in most of the dynamic probabilistic frameworks. In addition, we develop a new inference strategy, which first upward-and-backward propagates latent counts and then downward-and-forward samples variables, to enable efficient Gibbs sampling for the Recurrent-DBN. We apply the Recurrent-DBN to dynamic relational data problems. The extensive experiment results on real-world data validate the advantages of the Recurrent-DBN over the state-of-the-art models in interpretable latent structure discovery and improved link prediction performance.

Classifier calibration does not always go hand in hand with the classifier's ability to separate the classes. There are applications where good classifier calibration, i.e. the ability to produce accurate probability estimates, is more important than class separation. When the amount of data for training is limited, the traditional approach to improve calibration starts to crumble. In this article we show how generating more data for calibration is able to improve calibration algorithm performance in many cases where a classifier is not naturally producing well-calibrated outputs and the traditional approach fails. The proposed approach adds computational cost but considering that the main use case is with small data sets this extra computational cost stays insignificant and is comparable to other methods in prediction time. From the tested classifiers the largest improvement was detected with the random forest and naive Bayes classifiers. Therefore, the proposed approach can be recommended at least for those classifiers when the amount of data available for training is limited and good calibration is essential.

The point estimates of ReLU classification networks---arguably the most widely used neural network architecture---have been shown to yield arbitrarily high confidence far away from the training data. This architecture, in conjunction with a maximum a posteriori estimation scheme, is thus not calibrated nor robust. Approximate Bayesian inference has been empirically demonstrated to improve predictive uncertainty in neural networks, although the theoretical analysis of such Bayesian approximations is limited. We theoretically analyze approximate Gaussian posterior distributions on the weights of ReLU networks and show that they fix the overconfidence problem. Furthermore, we show that even a simplistic, thus cheap, Bayesian approximation, also fixes these issues. This indicates that a sufficient condition for a calibrated uncertainty on a ReLU network is ``to be a bit Bayesian''. These theoretical results validate the usage of last-layer Bayesian approximation and motivate a range of a fidelity-cost trade-off. We further validate these findings empirically via various standard experiments using common deep ReLU networks and Laplace approximations.

Graphical model selection in Markov random fields is a fundamental problem in statistics and machine learning. Two particularly prominent models, the Ising model and Gaussian model, have largely developed in parallel using different (though often related) techniques, and several practical algorithms with rigorous sample complexity bounds have been established for each. In this paper, we adapt a recently proposed algorithm of Klivans and Meka (FOCS, 2017), based on the method of multiplicative weight updates, from the Ising model to the Gaussian model, via non-trivial modifications to both the algorithm and its analysis. The algorithm enjoys a sample complexity bound that is qualitatively similar to others in the literature, has a low runtime $O(mp^2)$ in the case of $m$ samples and $p$ nodes, and can trivially be implemented in an online manner.