This paper develops computationally efficient data-driven model predictive control (MPC) for Agile quadrotor flight. Agile quadrotors in high-speed flights can experience high levels of aerodynamic effects. Modeling these turbulent aerodynamic effects is a cumbersome task and the resulting model may be overly complex and computationally infeasible. Combining Gaussian Process (GP) regression models with a simple dynamic model of the system has demonstrated significant improvements in control performance. However, direct integration of the GP models to the MPC pipeline poses a significant computational burden to the optimization process. Therefore, we present an approach to separate the GP models to the MPC pipeline by computing the model corrections using reference trajectory and the current state measurements prior to the online MPC optimization. This method has been validated in the Gazebo simulation environment and has demonstrated of up to $50\%$ reduction in trajectory tracking error, matching the performance of the direct GP integration method with improved computational efficiency.

Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small excess risk. If the true signal is $t$-sparse, information-theoretically, it is possible to achieve strong recovery guarantees with only $O(t\log n)$ samples. However, computationally efficient algorithms have sample complexity linear in (some variant of) the condition number of $\Sigma$. Classical algorithms such as the Lasso can require significantly more samples than necessary even if there is only a single sparse approximate dependency among the covariates. We provide a polynomial-time algorithm that, given $\Sigma$, automatically adapts the Lasso to tolerate a small number of approximate dependencies. In particular, we achieve near-optimal sample complexity for constant sparsity and if $\Sigma$ has few ``outlier'' eigenvalues. Our algorithm fits into a broader framework of feature adaptation for sparse linear regression with ill-conditioned covariates. With this framework, we additionally provide the first polynomial-factor improvement over brute-force search for constant sparsity $t$ and arbitrary covariance $\Sigma$.

A multivariate regression model of affine and diffeomorphic transformation sequences - FineMorphs - is presented. Leveraging concepts from shape analysis, model states are optimally "reshaped" by diffeomorphisms generated by smooth vector fields during learning. Affine transformations and vector fields are optimized within an optimal control setting, and the model can naturally reduce (or increase) dimensionality and adapt to large datasets via suboptimal vector fields. An existence proof of solution and necessary conditions for optimality for the model are derived. Experimental results on real datasets from the UCI repository are presented, with favorable results in comparison with state-of-the-art in the literature and densely-connected neural networks in TensorFlow.

In deep learning, often the training process finds an interpolator (a solution with 0 training loss), but the test loss is still low. This phenomenon, known as benign overfitting, is a major mystery that received a lot of recent attention. One common mechanism for benign overfitting is implicit regularization, where the training process leads to additional properties for the interpolator, often characterized by minimizing certain norms. However, even for a simple sparse linear regression problem $y = \beta^{*\top} x +\xi$ with sparse $\beta^*$, neither minimum $\ell_1$ or $\ell_2$ norm interpolator gives the optimal test loss. In this work, we give a different parametrization of the model which leads to a new implicit regularization effect that combines the benefit of $\ell_1$ and $\ell_2$ interpolators. We show that training our new model via gradient descent leads to an interpolator with near-optimal test loss. Our result is based on careful analysis of the training dynamics and provides another example of implicit regularization effect that goes beyond norm minimization.

Hydrothermal carbonization (HTC) is a process that converts biomass into versatile hydrochar without the need for prior drying. The physicochemical properties of hydrochar are influenced by biomass properties and processing parameters, making it challenging to optimize for specific applications through trial-and-error experiments. To save time and money, machine learning can be used to develop a model that characterizes hydrochar produced from different biomass sources under varying reaction processing parameters. Thus, this study aims to develop an inclusive model to characterize hydrochar using a database covering a range of biomass types and reaction processing parameters. The quality and quantity of hydrochar are predicted using two models (decision tree regression and support vector regression). The decision tree regression model outperforms the support vector regression model in terms of forecast accuracy (R2 > 0.88, RMSE < 6.848, and MAE < 4.718). Using an evolutionary algorithm, optimum inputs are identified based on cost functions provided by the selected model to optimize hydrochar for energy production, soil amendment, and pollutant adsorption, resulting in hydrochar yields of 84.31%, 84.91%, and 80.40%, respectively. The feature importance analysis reveals that biomass ash/carbon content and operating temperature are the primary factors affecting hydrochar production in the HTC process.

Co-pyrolysis of biomass feedstocks with polymeric wastes is a promising strategy for improving the quantity and quality parameters of the resulting liquid fuel. Numerous experimental measurements are typically conducted to find the optimal operating conditions. However, performing co-pyrolysis experiments is highly challenging due to the need for costly and lengthy procedures. Machine learning (ML) provides capabilities to cope with such issues by leveraging on existing data. This work aims to introduce an evolutionary ML approach to quantify the (by)products of the biomass-polymer co-pyrolysis process. A comprehensive dataset covering various biomass-polymer mixtures under a broad range of process conditions is compiled from the qualified literature. The database was subjected to statistical analysis and mechanistic discussion. The input features are constructed using an innovative approach to reflect the physics of the process. The constructed features are subjected to principal component analysis to reduce their dimensionality. The obtained scores are introduced into six ML models. Gaussian process regression model tuned by particle swarm optimization algorithm presents better prediction performance (R2 > 0.9, MAE < 0.03, and RMSE < 0.06) than other developed models. The multi-objective particle swarm optimization algorithm successfully finds optimal independent parameters.

Autonomous cars are indispensable when humans go further down the hands-free route. Although existing literature highlights that the acceptance of the autonomous car will increase if it drives in a human-like manner, sparse research offers the naturalistic experience from a passenger's seat perspective to examine the humanness of current autonomous cars. The present study tested whether the AI driver could create a human-like ride experience for passengers based on 69 participants' feedback in a real-road scenario. We designed a ride experience-based version of the non-verbal Turing test for automated driving. Participants rode in autonomous cars (driven by either human or AI drivers) as a passenger and judged whether the driver was human or AI. The AI driver failed to pass our test because passengers detected the AI driver above chance. In contrast, when the human driver drove the car, the passengers' judgement was around chance. We further investigated how human passengers ascribe humanness in our test. Based on Lewin's field theory, we advanced a computational model combining signal detection theory with pre-trained language models to predict passengers' humanness rating behaviour. We employed affective transition between pre-study baseline emotions and corresponding post-stage emotions as the signal strength of our model. Results showed that the passengers' ascription of humanness would increase with the greater affective transition. Our study suggested an important role of affective transition in passengers' ascription of humanness, which might become a future direction for autonomous driving.

The shift between the training and testing distributions is commonly due to sample selection bias, a type of bias caused by non-random sampling of examples to be included in the training set. Although there are many approaches proposed to learn a classifier under sample selection bias, few address the case where a subset of labels in the training set are missing-not-at-random (MNAR) as a result of the selection process. In statistics, Greene's method formulates this type of sample selection with logistic regression as the prediction model. However, we find that simply integrating this method into a robust classification framework is not effective for this bias setting. In this paper, we propose BiasCorr, an algorithm that improves on Greene's method by modifying the original training set in order for a classifier to learn under MNAR sample selection bias. We provide theoretical guarantee for the improvement of BiasCorr over Greene's method by analyzing its bias. Experimental results on real-world datasets demonstrate that BiasCorr produces robust classifiers and can be extended to outperform state-of-the-art classifiers that have been proposed to train under sample selection bias.

Signature transforms are iterated path integrals of continuous and discrete-time time series data, and their universal nonlinearity linearizes the problem of feature selection. This paper revisits the consistency issue of Lasso regression for the signature transform, both theoretically and numerically. Our study shows that, for processes and time series that are closer to Brownian motion or random walk with weaker inter-dimensional correlations, the Lasso regression is more consistent for their signatures defined by It\^o integrals; for mean reverting processes and time series, their signatures defined by Stratonovich integrals have more consistency in the Lasso regression. Our findings highlight the importance of choosing appropriate definitions of signatures and stochastic models in statistical inference and machine learning.

Weighting methods in causal inference have been widely used to achieve a desirable level of covariate balancing. However, the existing weighting methods have desirable theoretical properties only when a certain model, either the propensity score or outcome regression model, is correctly specified. In addition, the corresponding estimators do not behave well for finite samples due to large variance even when the model is correctly specified. In this paper, we consider to use the integral probability metric (IPM), which is a metric between two probability measures, for covariate balancing. Optimal weights are determined so that weighted empirical distributions for the treated and control groups have the smallest IPM value for a given set of discriminators. We prove that the corresponding estimator can be consistent without correctly specifying any model (neither the propensity score nor the outcome regression model). In addition, we empirically show that our proposed method outperforms existing weighting methods with large margins for finite samples.