A counterfactual distribution is the probability distribution of a random variable under a hypothetical scenario that differs from the observed reality. "What would have been the outcome for this individual if they had received a different treatment?" is an example of a counterfactual question. Here the personal data of the individual constitute the evidence that specifies the observed reality, and the interest lies in the distribution of the outcome under a hypothetical treatment. Counterfactual questions belong to the third and highest level in the causal hierarchy (Shpitser and Pearl, 2008) and are in general more difficult than associational (first level) or interventional (second level) questions. Algorithms for checking the identifiability of counterfactual queries from observational and experimental data have been developed (Shpitser and Pearl, 2007; Shpitser and Sherman, 2018; Correa et al., 2021) and implemented (Tikka, 2022).

Dueling bandits are widely used to model preferential feedback prevalent in many applications such as recommendation systems and ranking. In this paper, we study the Borda regret minimization problem for dueling bandits, which aims to identify the item with the highest Borda score while minimizing the cumulative regret. We propose a rich class of generalized linear dueling bandit models, which cover many existing models. We first prove a regret lower bound of order $\Omega(d^{2/3} T^{2/3})$ for the Borda regret minimization problem, where $d$ is the dimension of contextual vectors and $T$ is the time horizon. To attain this lower bound, we propose an explore-then-commit type algorithm for the stochastic setting, which has a nearly matching regret upper bound $\tilde{O}(d^{2/3} T^{2/3})$. We also propose an EXP3-type algorithm for the adversarial linear setting, where the underlying model parameter can change at each round. Our algorithm achieves an $\tilde{O}(d^{2/3} T^{2/3})$ regret, which is also optimal. Empirical evaluations on both synthetic data and a simulated real-world environment are conducted to corroborate our theoretical analysis.

Hybrid modeling, that is the combination of data-driven and theory-driven modeling, has recently raised a lot of attention. The integration of physical models in machine learning has indeed demonstrated promising properties such as improved interpolation and extrapolation capabilities and increased interpretability [1, 2]. Conventional machine learning models learn correlations, from a training data set, in order to map observations to targets or latent representations, with the hope to generalize to new data. While many different models could perfectly fit the training data, the assumptions made during the learning process (from the model architecture to the learning algorithm itself), sometimes called inductive biases [3, 4], are crucial to obtain high generalization performances. In contrast, hybrid models are partially grounded on deductive biases, i.e. assumptions derived, in our context, from physics models that generalize, by nature, to out-of-distribution data. Therefore, in various fields for which the data distribution is governed by physical laws, such as fluid dynamics, thermodynamics or solid mechanics, hybrid modeling has recently become a hot topic [5, 6, 7].

We consider the problem of estimating the marginal independence structure of a Bayesian network from observational data in the form of an undirected graph called the unconditional dependence graph. We show that unconditional dependence graphs of Bayesian networks correspond to the graphs having equal independence and intersection numbers. Using this observation, a Gr\"obner basis for a toric ideal associated to unconditional dependence graphs of Bayesian networks is given and then extended by additional binomial relations to connect the space of all such graphs. An MCMC method, called GrUES (Gr\"obner-based Unconditional Equivalence Search), is implemented based on the resulting moves and applied to synthetic Gaussian data. GrUES recovers the true marginal independence structure via a penalized maximum likelihood or MAP estimate at a higher rate than simple independence tests while also yielding an estimate of the posterior, for which the $20\%$ HPD credible sets include the true structure at a high rate for data-generating graphs with density at least $0.5$.

The hierarchy of global and local planners is one of the most commonly utilized system designs in autonomous robot navigation. While the global planner generates a reference path from the current to goal locations based on the pre-built static map, the local planner produces a kinodynamic trajectory to follow the reference path while avoiding perceived obstacles. To account for unforeseen or dynamic obstacles not present on the pre-built map, ``when to replan'' the reference path is critical for the success of safe and efficient navigation. However, determining the ideal timing to execute replanning in such partially unknown environments still remains an open question. In this work, we first conduct an extensive simulation experiment to compare several common replanning strategies and confirm that effective strategies are highly dependent on the environment as well as the global and local planners. Based on this insight, we derive a new adaptive replanning strategy based on deep reinforcement learning, which can learn from experience to decide appropriate replanning timings in the given environment and planning setups. Our experimental results demonstrate that the proposed replanner can perform on par or even better than the current best-performing strategies in multiple situations regarding navigation robustness and efficiency.

Modern ML applications increasingly rely on complex deep learning models and large datasets. There has been an exponential growth in the amount of computation needed to train the largest models. Therefore, to scale computation and data, these models are inevitably trained in a distributed manner in clusters of nodes, and their updates are aggregated before being applied to the model. However, a distributed setup is prone to Byzantine failures of individual nodes, components, and software. With data augmentation added to these settings, there is a critical need for robust and efficient aggregation systems. We define the quality of workers as reconstruction ratios $\in (0,1]$, and formulate aggregation as a Maximum Likelihood Estimation procedure using Beta densities. We show that the Regularized form of log-likelihood wrt subspace can be approximately solved using iterative least squares solver, and provide convergence guarantees using recent Convex Optimization landscape results. Our empirical findings demonstrate that our approach significantly enhances the robustness of state-of-the-art Byzantine resilient aggregators. We evaluate our method in a distributed setup with a parameter server, and show simultaneous improvements in communication efficiency and accuracy across various tasks. The code is publicly available at https://github.com/hamidralmasi/FlagAggregator

Learning from label proportions (LLP) is a weakly supervised classification problem where data points are grouped into bags, and the label proportions within each bag are observed instead of the instance-level labels. The task is to learn a classifier to predict the individual labels of future individual instances. Prior work on LLP for multi-class data has yet to develop a theoretically grounded algorithm. In this work, we provide a theoretically grounded approach to LLP based on a reduction to learning with label noise, using the forward correction (FC) loss of \citet{Patrini2017MakingDN}. We establish an excess risk bound and generalization error analysis for our approach, while also extending the theory of the FC loss which may be of independent interest. Our approach demonstrates improved empirical performance in deep learning scenarios across multiple datasets and architectures, compared to the leading existing methods.

The quintessential learning algorithm of empirical risk minimization (ERM) is known to fail in various settings for which uniform convergence does not characterize learning. It is therefore unsurprising that the practice of machine learning is rife with considerably richer algorithmic techniques for successfully controlling model capacity. Nevertheless, no such technique or principle has broken away from the pack to characterize optimal learning in these more general settings. The purpose of this work is to characterize the role of regularization in perhaps the simplest setting for which ERM fails: multiclass learning with arbitrary label sets. Using one-inclusion graphs (OIGs), we exhibit optimal learning algorithms that dovetail with tried-and-true algorithmic principles: Occam's Razor as embodied by structural risk minimization (SRM), the principle of maximum entropy, and Bayesian reasoning. Most notably, we introduce an optimal learner which relaxes structural risk minimization on two dimensions: it allows the regularization function to be "local" to datapoints, and uses an unsupervised learning stage to learn this regularizer at the outset. We justify these relaxations by showing that they are necessary: removing either dimension fails to yield a near-optimal learner. We also extract from OIGs a combinatorial sequence we term the Hall complexity, which is the first to characterize a problem's transductive error rate exactly. Lastly, we introduce a generalization of OIGs and the transductive learning setting to the agnostic case, where we show that optimal orientations of Hamming graphs -- judged using nodes' outdegrees minus a system of node-dependent credits -- characterize optimal learners exactly. We demonstrate that an agnostic version of the Hall complexity again characterizes error rates exactly, and exhibit an optimal learner using maximum entropy programs.

In the field of object classification, identification based on object variations is a challenge in itself. Variations include shape, size, color, and texture, these can cause problems in recognizing and distinguishing objects accurately. The purpose of this research is to develop a classification method so that objects can be accurately identified. The proposed classification model uses Voting and Combined Classifier, with Random Forest, K-NN, Decision Tree, SVM, and Naive Bayes classification methods. The test results show that the voting method and Combined Classifier obtain quite good results with each of them, ensemble voting with an accuracy value of 92.4%, 78.6% precision, 95.2% recall, and 86.1% F1-score. While the combined classifier with an accuracy value of 99.3%, a precision of 97.6%, a recall of 100%, and a 98.8% F1-score. Based on the test results, it can be concluded that the use of the Combined Classifier and voting methods is proven to increase the accuracy value. The contribution of this research increases the effectiveness of the Ensemble Learning method, especially the voting ensemble method and the Combined Classifier in increasing the accuracy of object classification in image processing.

This paper presents an interpretable review of various machine learning and deep learning models to predict the maintenance of aircraft engine to avoid any kind of disaster. One of the advantages of the strategy is that it can work with modest datasets. In this study, sensor data is utilized to predict aircraft engine failure within a predetermined number of cycles using LSTM, Bi-LSTM, RNN, Bi-RNN GRU, Random Forest, KNN, Naive Bayes, and Gradient Boosting. We explain how deep learning and machine learning can be used to generate predictions in predictive maintenance using a straightforward scenario with just one data source. We applied lime to the models to help us understand why machine learning models did not perform well than deep learning models. An extensive analysis of the model's behavior is presented for several test data to understand the black box scenario of the models. A lucrative accuracy of 97.8%, 97.14%, and 96.42% are achieved by GRU, Bi-LSTM, and LSTM respectively which denotes the capability of the models to predict maintenance at an early stage.