This paper addresses the problem of precisely estimating the parameters of a stochastic model corresponding to branching processes. A branching process is a stochastic process consisting of collections of random variables indexed by the natural numbers. Branching processes are often used to describe population models Jagers (1989) and Athreya and Ney (2012); for example, models in the population genetics showing the genetic drift Burden and Simon (2016) Chen et al. (2017). In contrast to statistical approaches, branching processes enable the study of the dynamics of cell evolution and, as a consistence, have become a popular approach to cancer cell evolution research West et al., 2016. However, particularly in the case of cancer cell evolution, as well as in branching processes in general, the ultimate extinction of a population often occurs Devroye (1998). It is for this reason that with the initial uniform distribution of parameters, branching processes models tend to yield unevenly distributed data consisting of sparse and dense regions. The stochastic nature of the data is an another obstacle in estimating the parameters of a branching processes model, especially in the case of cancer cell evolution Nagornov et al. (2021). Moreover, simulations, based on a model of cell mutations, population evolution, and tumor/cancer subpopulations, commonly lead to the emergence of many clones and rarely to the appearance of cancer cells.

Fuzzy Logic isn't often mentioned in the same room as Artificial Intelligence (AI). Pardon the pun, but most people find the idea of fuzzy logic to be fuzzy. However fuzzy logic has been working behind the scenes and bringing forth amazing technological advances for more than two decades. Fuzzy logic is a rule-based system that can rely on the practical experience of a data scientist or an expert. Fuzzy logic is a form of artificial intelligence, thus it is considered a subset of AI. Since it is performing a form of decision making, it can be included as a member of the AI family which includes Machine Learning and Deep Learning.

Generative Adversarial Networks (GANs) software is software for producing forgeries and imitations of data (aka synthetic data, fake data). Human beings have been making fakes, with good or evil intent, of almost everything they possibly can, since the beginning of the human race. Thus, perhaps not too surprisingly, GAN software has been widely used since it was first proposed in this amazingly recent 2014 paper. To gauge how widely GAN software has been used so far, see, for example, this 2019 article entitled "18 Impressive Applications of Generative Adversarial Networks (GANs)" Sounds (voices, music,…), Images (realistic pictures, paintings, drawings, handwriting, …), Text,etc. The forgeries can be tweaked so that they range from being very similar to the originals, to being whimsical exaggerations thereof.

Aqueous hydrolysis is used to chemically recycle polyethylene terephthalate (PET) due to the production of high-quality terephthalic acid (TPA), the PET monomer. PET hydrolysis depends on various reaction conditions including PET size, catalyst concentration, reaction temperature, etc. So, modeling PET hydrolysis by considering the effective factors can provide useful information for material scientists to specify how to design and run these reactions. It will save time, energy, and materials by optimizing the hydrolysis conditions. Machine learning algorithms enable to design models to predict output results. For the first time, 381 experimental data were gathered to model the aqueous hydrolysis of PET. Effective reaction conditions on PET hydrolysis were connected to TPA yield. The logistic regression was applied to rank the reaction conditions. Two algorithms were proposed, artificial neural network multilayer perceptron (ANN-MLP) and adaptive network-based fuzzy inference system (ANFIS). The dataset was divided into training and testing sets to train and test the models, respectively. The models predicted TPA yield sufficiently where the ANFIS model outperformed. R-squared (R2) and Root Mean Square Error (RMSE) loss functions were employed to measure the efficiency of the models and evaluate their performance.

Applications of neural networks have achieved great success in various fields. A major extension of the standard neural networks is to make them stochastic, namely, to make the output a random function of the input. In a broad sense, stochastic neural networks include neural networks trained with dropout (Srivastava et al., 2014; Gal & Ghahramani, 2016), Bayesian networks (Mackay, 1992), variational autoencoders (VAE) (Kingma & Welling, 2013), and generative adversarial networks (Goodfellow et al., 2014). There are many reasons why one wants to make a neural network stochastic. Two main reasons are (1) regularization and (2) distribution modeling.

Random partition models are widely used in Bayesian methods for various clustering tasks, such as mixture models, topic models, and community detection problems. While the number of clusters induced by random partition models has been studied extensively, another important model property regarding the balancedness of cluster sizes has been largely neglected. We formulate a framework to define and theoretically study the balancedness of exchangeable random partition models, by analyzing how a model assigns probabilities to partitions with different levels of balancedness. We demonstrate that the "rich-get-richer" characteristic of many existing popular random partition models is an inevitable consequence of two common assumptions: product-form exchangeability and projectivity. We propose a principled way to compare the balancedness of random partition models, which gives a better understanding of what model works better and what doesn't for different applications. We also introduce the "rich-get-poorer" random partition models and illustrate their application to entity resolution tasks.

In recent years there has been a growing interest in the estimation of causal effects using machine learning algorithms, particularly in the field of economics (Athey, 2018). The newly emerging synthesis of machine learning methods with causal inference has a large potential for a more comprehensive estimation of causal effects (Lechner, 2018). On the one hand, it enables a more flexible estimation of average effects which are of main interest in microeconometrics (Imbens & Wooldridge, 2009). On the other hand, it advances the estimation beyond the average effects and allows for a systematic analysis of effect heterogeneity (Athey & Imbens, 2017). Both of these aspects contribute to a better description of the causal mechanisms and thus to a possibly more efficient treatment allocation (Zhao, Zeng, Rush, & Kosorok, 2012; Kitagawa & Tetenov, 2018; Athey & Wager, 2021; Nie, Brunskill, & Wager, 2021). Hence, applied empirical researchers can greatly benefit from the usage of machine learning methods ranging from evaluation of public policies and business decisions to designing personalized interventions (Andini, Ciani, de Blasio, D'Ignazio, & Salvestrini, 2018; Bansak et al., 2018). Machine learning estimators as such are, however, primarily designed for prediction problems and thus cannot be used directly for causal inference. Therefore, new approaches for the estimation of causal parameters using machine learning emerged (see Athey & Imbens, 2019, for an overview). In particular, the development of the so-called meta-learners have received considerable attention (see e.g.

We consider offline Imitation Learning from corrupted demonstrations where a constant fraction of data can be noise or even arbitrary outliers. Classical approaches such as Behavior Cloning assumes that demonstrations are collected by an presumably optimal expert, hence may fail drastically when learning from corrupted demonstrations. We propose a novel robust algorithm by minimizing a Median-of-Means (MOM) objective which guarantees the accurate estimation of policy, even in the presence of constant fraction of outliers. Our theoretical analysis shows that our robust method in the corrupted setting enjoys nearly the same error scaling and sample complexity guarantees as the classical Behavior Cloning in the expert demonstration setting. Our experiments on continuous-control benchmarks validate that our method exhibits the predicted robustness and effectiveness, and achieves competitive results compared to existing imitation learning methods.

Reasoning about uncertainty is vital in many real-life autonomous systems. However, current state-of-the-art planning algorithms cannot either reason about uncertainty explicitly, or do so with a high computational burden. Here, we focus on making informed decisions efficiently, using reward functions that explicitly deal with uncertainty. We formulate an approximation, namely an abstract observation model, that uses an aggregation scheme to alleviate computational costs. We derive bounds on the expected information-theoretic reward function and, as a consequence, on the value function. We then propose a method to refine aggregation to achieve identical action selection with a fraction of the computational time.

Approximate Bayesian computation (ABC) is a popular likelihood-free inference method for models with intractable likelihood functions. As ABC methods usually rely on comparing summary statistics of observed and simulated data, the choice of the statistics is crucial. This choice involves a trade-off between loss of information and dimensionality reduction, and is often determined based on domain knowledge. However, handcrafting and selecting suitable statistics is a laborious task involving multiple trial-and-error steps. In this work, we introduce an active learning method for ABC statistics selection which reduces the domain expert's work considerably. By involving the experts, we are able to handle misspecified models, unlike the existing dimension reduction methods. Moreover, empirical results show better posterior estimates than with existing methods, when the simulation budget is limited.