The book attempts to introduce a gentle introduction to the field of Facial Micro Expressions Recognition (FMER) using Color and Depth images, with the aid of MATLAB programming environment. FMER is a subset of image processing and it is a multidisciplinary topic to analysis. So, it requires familiarity with other topics of Artifactual Intelligence (AI) such as machine learning, digital image processing, psychology and more. So, it is a great opportunity to write a book which covers all of these topics for beginner to professional readers in the field of AI and even without having background of AI. Our goal is to provide a standalone introduction in the field of MFER analysis in the form of theorical descriptions for readers with no background in image processing with reproducible Matlab practical examples. Also, we describe any basic definitions for FMER analysis and MATLAB library which is used in the text, that helps final reader to apply the experiments in the real-world applications. We believe that this book is suitable for students, researchers, and professionals alike, who need to develop practical skills, along with a basic understanding of the field. We expect that, after reading this book, the reader feels comfortable with different key stages such as color and depth image processing, color and depth image representation, classification, machine learning, facial micro-expressions recognition, feature extraction and dimensionality reduction. The book attempts to introduce a gentle introduction to the field of Facial Micro Expressions Recognition (FMER) using Color and Depth images, with the aid of MATLAB programming environment.

We address the problem of identifiability of an arbitrary conditional causal effect given both the causal graph and a set of any observational and/or interventional distributions of the form $Q[S]:=P(S|do(V\setminus S))$, where $V$ denotes the set of all observed variables and $S\subseteq V$. We call this problem conditional generalized identifiability (c-gID in short) and prove the completeness of Pearl's $do$-calculus for the c-gID problem by providing sound and complete algorithm for the c-gID problem. This work revisited the c-gID problem in Lee et al. [2020], Correa et al. [2021] by adding explicitly the positivity assumption which is crucial for identifiability. It extends the results of [Lee et al., 2019, Kivva et al., 2022] on general identifiability (gID) which studied the problem for unconditional causal effects and Shpitser and Pearl [2006b] on identifiability of conditional causal effects given merely the observational distribution $P(\mathbf{V})$ as our algorithm generalizes the algorithms proposed in [Kivva et al., 2022] and [Shpitser and Pearl, 2006b].

Discount regularization, using a shorter planning horizon when calculating the optimal policy, is a popular choice to restrict planning to a less complex set of policies when estimating an MDP from sparse or noisy data (Jiang et al., 2015). It is commonly understood that discount regularization functions by de-emphasizing or ignoring delayed effects. In this paper, we reveal an alternate view of discount regularization that exposes unintended consequences. We demonstrate that planning under a lower discount factor produces an identical optimal policy to planning using any prior on the transition matrix that has the same distribution for all states and actions. In fact, it functions like a prior with stronger regularization on state-action pairs with more transition data. This leads to poor performance when the transition matrix is estimated from data sets with uneven amounts of data across state-action pairs. Our equivalence theorem leads to an explicit formula to set regularization parameters locally for individual state-action pairs rather than globally. We demonstrate the failures of discount regularization and how we remedy them using our state-action-specific method across simple empirical examples as well as a medical cancer simulator.

Recent years have seen a growing interest in methods for predicting a variable of interest, such as a subject's diagnosis, from medical images. Methods based on discriminative modeling excel at making accurate predictions, but are challenged in their ability to explain their decisions in anatomically meaningful terms. In this paper, we propose a simple technique for single-subject prediction that is inherently interpretable. It augments the generative models used in classical human brain mapping techniques, in which cause-effect relations can be encoded, with a multivariate noise model that captures dominant spatial correlations. Experiments demonstrate that the resulting model can be efficiently inverted to make accurate subject-level predictions, while at the same time offering intuitive causal explanations of its inner workings. The method is easy to use: training is fast for typical training set sizes, and only a single hyperparameter needs to be set by the user. Our code is available at https://github.com/chiara-mauri/Interpretable-subject-level-prediction.

Causal effect estimation from data typically requires assumptions about the cause-effect relations either explicitly in the form of a causal graph structure within the Pearlian framework, or implicitly in terms of (conditional) independence statements between counterfactual variables within the potential outcomes framework. When the treatment variable and the outcome variable are confounded, front-door adjustment is an important special case where, given the graph, causal effect of the treatment on the target can be estimated using post-treatment variables. However, the exact formula for front-door adjustment depends on the structure of the graph, which is difficult to learn in practice. In this work, we provide testable conditional independence statements to compute the causal effect using front-door-like adjustment without knowing the graph under limited structural side information. We show that our method is applicable in scenarios where knowing the Markov equivalence class is not sufficient for causal effect estimation. We demonstrate the effectiveness of our method on a class of random graphs as well as real causal fairness benchmarks.

In this paper, we present a novel characterization of the smoothness of a model based on basic principles of Large Deviation Theory. In contrast to prior work, where the smoothness of a model is normally characterized by a real value (e.g., the weights' norm), we show that smoothness can be described by a simple real-valued function. Based on this concept of smoothness, we propose an unifying theoretical explanation of why some interpolators generalize remarkably well and why a wide range of modern learning techniques (i.e., stochastic gradient descent, $\ell_2$-norm regularization, data augmentation, invariant architectures, and overparameterization) are able to find them. The emergent conclusion is that all these methods provide complimentary procedures that bias the optimizer to smoother interpolators, which, according to this theoretical analysis, are the ones with better generalization error.

Algorithms for causal discovery have recently undergone rapid advances and increasingly draw on flexible nonparametric methods to process complex data. With these advances comes a need for adequate empirical validation of the causal relationships learned by different algorithms. However, for most real data sources true causal relations remain unknown. This issue is further compounded by privacy concerns surrounding the release of suitable high-quality data. To help address these challenges, we gather a complex dataset comprising measurements from an assembly line in a manufacturing context. This line consists of numerous physical processes for which we are able to provide ground truth causal relationships on the basis of a detailed study of the underlying physics. We use the assembly line data and associated ground truth information to build a system for generation of semisynthetic manufacturing data that supports benchmarking of causal discovery methods. To accomplish this, we employ distributional random forests in order to flexibly estimate and represent conditional distributions that may be combined into joint distributions that strictly adhere to a causal model over the observed variables. The estimated conditionals and tools for data generation are made available in our Python library $\texttt{causalAssembly}$. Using the library, we showcase how to benchmark several well-known causal discovery algorithms.

First Order Bayesian Optimization (FOBO) is a sample efficient sequential approach to find the global maxima of an expensive-to-evaluate black-box objective function by suitably querying for the function and its gradient evaluations. Such methods assume Gaussian process (GP) models for both, the function and its gradient, and use them to construct an acquisition function that identifies the next query point. In this paper, we propose a class of practical FOBO algorithms that efficiently utilizes the information from the gradient GP to identify potential query points with zero gradients. We construct a multi-level acquisition function where in the first step, we optimize a lower level acquisition function with multiple restarts to identify potential query points with zero gradient value. We then use the upper level acquisition function to rank these query points based on their function values to potentially identify the global maxima. As a final step, the potential point of maxima is chosen as the actual query point. We validate the performance of our proposed algorithms on several test functions and show that our algorithms outperform state-of-the-art FOBO algorithms. We also illustrate the application of our algorithms in finding optimal set of hyper-parameters in machine learning and in learning the optimal policy in reinforcement learning tasks.

In this paper, we introduce BNN-DP, an efficient algorithmic framework for analysis of adversarial robustness of Bayesian Neural Networks (BNNs). Given a compact set of input points $T\subset \mathbb{R}^n$, BNN-DP computes lower and upper bounds on the BNN's predictions for all the points in $T$. The framework is based on an interpretation of BNNs as stochastic dynamical systems, which enables the use of Dynamic Programming (DP) algorithms to bound the prediction range along the layers of the network. Specifically, the method uses bound propagation techniques and convex relaxations to derive a backward recursion procedure to over-approximate the prediction range of the BNN with piecewise affine functions. The algorithm is general and can handle both regression and classification tasks. On a set of experiments on various regression and classification tasks and BNN architectures, we show that BNN-DP outperforms state-of-the-art methods by up to four orders of magnitude in both tightness of the bounds and computational efficiency.

In many domains, autoregressive models can attain high likelihood on the task of predicting the next observation. However, this maximum-likelihood (MLE) objective does not necessarily match a downstream use-case of autoregressively generating high-quality sequences. The MLE objective weights sequences proportionally to their frequency under the data distribution, with no guidance for the model's behaviour out of distribution (OOD): leading to compounding error during autoregressive generation. In order to address this compounding error problem, we formulate sequence generation as an imitation learning (IL) problem. This allows us to minimize a variety of divergences between the distribution of sequences generated by an autoregressive model and sequences from a dataset, including divergences with weight on OOD generated sequences. The IL framework also allows us to incorporate backtracking by introducing a backspace action into the generation process. This further mitigates the compounding error problem by allowing the model to revert a sampled token if it takes the sequence OOD. Our resulting method, SequenceMatch, can be implemented without adversarial training or major architectural changes. We identify the SequenceMatch-$\chi^2$ divergence as a more suitable training objective for autoregressive models which are used for generation. We show that empirically, SequenceMatch training leads to improvements over MLE on text generation with language models.