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Join order selection is a sub-field of query optimization that aims to find the optimal join order for an SQL query with the minimum cost. The challenge lies in the exponentially growing search space as the number of tables increases, making exhaustive enumeration impractical. Traditional optimizers use static heuristics to prune the search space, but they often fail to adapt to changes or improve based on feedback from the DBMS. Recent research addresses these limitations with Deep Reinforcement Learning (DRL), allowing models to use feedback to dynamically search for better join orders and enhance performance over time. Existing research primarily focuses on capturing join order sequences and their representations at various levels, with limited comparative analysis of reinforcement learning methods. In this paper, we propose GTDD, a novel framework that integrates Graph Neural Networks (GNN), Treestructured Long Short-Term Memory (Tree LSTM), and DuelingDQN. We conduct a series of experiments that demonstrate a clear advantage of GTDD over state-of the-art techniques.

Feature selection is crucial for pinpointing relevant features in high-dimensional datasets, mitigating the 'curse of dimensionality,' and enhancing machine learning performance. Traditional feature selection methods for classification use data from all classes to select features for each class. This paper explores feature selection methods that select features for each class separately, using class models based on low-rank generative methods and introducing a signal-to-noise ratio (SNR) feature selection criterion. This novel approach has theoretical true feature recovery guarantees under certain assumptions and is shown to outperform some existing feature selection methods on standard classification datasets.

In structured additive distributional regression, the conditional distribution of the response variables given the covariate information and the vector of model parameters is modelled using a P-parametric probability density function where each parameter is modelled through a linear predictor and a bijective response function that maps the domain of the predictor into the domain of the parameter. We present a method to perform inference in structured additive distributional regression using stochastic variational inference. We propose two strategies for constructing a multivariate Gaussian variational distribution to estimate the posterior distribution of the regression coefficients. The first strategy leverages covariate information and hyperparameters to learn both the location vector and the precision matrix. The second strategy tackles the complexity challenges of the first by initially assuming independence among all smooth terms and then introducing correlations through an additional set of variational parameters. Furthermore, we present two approaches for estimating the smoothing parameters. The first treats them as free parameters and provides point estimates, while the second accounts for uncertainty by applying a variational approximation to the posterior distribution. Our model was benchmarked against state-of-the-art competitors in logistic and gamma regression simulation studies. Finally, we validated our approach by comparing its posterior estimates to those obtained using Markov Chain Monte Carlo on a dataset of patents from the biotechnology/pharmaceutics and semiconductor/computer sectors.

Noisy matrix completion has attracted significant attention due to its applications in recommendation systems, signal processing and image restoration. Most existing works rely on (weighted) least squares methods under various low-rank constraints. However, minimizing the sum of squared residuals is not always efficient, as it may ignore the potential structural information in the residuals.In this study, we propose a novel residual spectral matching criterion that incorporates not only the numerical but also locational information of residuals. This criterion is the first in noisy matrix completion to adopt the perspective of low-rank perturbation of random matrices and exploit the spectral properties of sparse random matrices. We derive optimal statistical properties by analyzing the spectral properties of sparse random matrices and bounding the effects of low-rank perturbations and partial observations. Additionally, we propose algorithms that efficiently approximate solutions by constructing easily computable pseudo-gradients. The iterative process of the proposed algorithms ensures convergence at a rate consistent with the optimal statistical error bound. Our method and algorithms demonstrate improved numerical performance in both simulated and real data examples, particularly in environments with high noise levels.

Kernel methods map data into high-dimensional spaces, enabling linear algorithms to learn nonlinear functions without explicitly storing the feature vectors. Quantum kernel methods promise efficient learning by encoding feature maps into exponentially large Hilbert spaces inherent in quantum systems. In this work we implement quantum kernels on a 10-qubit star-topology register in a nuclear magnetic resonance (NMR) platform. We experimentally encode classical data in the evolution of multiple quantum coherence orders using data-dependent unitary transformations and then demonstrate one-dimensional regression and two-dimensional classification tasks. By extending the register to a double-layered star configuration, we propose an extended quantum kernel to handle non-parametrized operator inputs. By numerically simulating the extended quantum kernel, we show classification of entangling and nonentangling unitaries. These results confirm that quantum kernels exhibit strong capabilities in classical as well as quantum machine learning tasks.

Holographic multiple-input multiple-output (HMIMO) utilizes a compact antenna array to form a nearly continuous aperture, thereby enhancing higher capacity and more flexible configurations compared with conventional MIMO systems, making it attractive in current scientific research. Key questions naturally arise regarding the potential of HMIMO to surpass Shannon's theoretical limits and how far its capabilities can be extended. However, the traditional Shannon information theory falls short in addressing these inquiries because it only focuses on the information itself while neglecting the underlying carrier, electromagnetic (EM) waves, and environmental interactions. To fill up the gap between the theoretical analysis and the practical application for HMIMO systems, we introduce electromagnetic information theory (EIT) in this paper. This paper begins by laying the foundation for HMIMO-oriented EIT, encompassing EM wave equations and communication regions. In the context of HMIMO systems, the resultant physical limitations are presented, involving Chu's limit, Harrington's limit, Hannan's limit, and the evaluation of coupling effects. Field sampling and HMIMO-assisted oversampling are also discussed to guide the optimal HMIMO design within the EIT framework. To comprehensively depict the EM-compliant propagation process, we present the approximate and exact channel modeling approaches in near-/far-field zones. Furthermore, we discuss both traditional Shannon's information theory, employing the probabilistic method, and Kolmogorov information theory, utilizing the functional analysis, for HMIMO-oriented EIT systems.

Gaussian Process differential equations (GPODE) have recently gained momentum due to their ability to capture dynamics behavior of systems and also represent uncertainty in predictions. Prior work has described the process of training the hyperparameters and, thereby, calibrating GPODE to data. How to design efficient algorithms to collect data for training GPODE models is still an open field of research. Nevertheless high-quality training data is key for model performance. Furthermore, data collection leads to time-cost and financial-cost and might in some areas even be safety critical to the system under test. Therefore, algorithms for safe and efficient data collection are central for building high quality GPODE models. Our novel Safe Active Learning (SAL) for GPODE algorithm addresses this challenge by suggesting a mechanism to propose efficient and non-safety-critical data to collect. SAL GPODE does so by sequentially suggesting new data, measuring it and updating the GPODE model with the new data. In this way, subsequent data points are iteratively suggested. The core of our SAL GPODE algorithm is a constrained optimization problem maximizing information of new data for GPODE model training constrained by the safety of the underlying system. We demonstrate our novel SAL GPODE's superiority compared to a standard, non-active way of measuring new data on two relevant examples.

Multimodal intention understanding (MIU) is an indispensable component of human expression analysis (e.g., sentiment or humor) from heterogeneous modalities, including visual postures, linguistic contents, and acoustic behaviors. Existing works invariably focus on designing sophisticated structures or fusion strategies to achieve impressive improvements. Unfortunately, they all suffer from the subject variation problem due to data distribution discrepancies among subjects. Concretely, MIU models are easily misled by distinct subjects with different expression customs and characteristics in the training data to learn subject-specific spurious correlations, significantly limiting performance and generalizability across uninitiated subjects.Motivated by this observation, we introduce a recapitulative causal graph to formulate the MIU procedure and analyze the confounding effect of subjects. Then, we propose SuCI, a simple yet effective causal intervention module to disentangle the impact of subjects acting as unobserved confounders and achieve model training via true causal effects. As a plug-and-play component, SuCI can be widely applied to most methods that seek unbiased predictions. Comprehensive experiments on several MIU benchmarks clearly demonstrate the effectiveness of the proposed module.

Not many tests exist for testing the equality for two or more multivariate distributions with compositional data, perhaps due to their constrained sample space. At the moment, there is only one test suggested that relies upon random projections. We propose a novel test termed {\alpha}-Energy Based Test ({\alpha}-EBT) to compare the multivariate distributions of two (or more) compositional data sets. Similar to the aforementioned test, the new test makes no parametric assumptions about the data and, based on simulation studies it exhibits higher power levels.

The Knaster-Tarski theorem, also known as Tarski's theorem, guarantees that every monotone function defined on a complete lattice has a fixed point. We analyze the query complexity of finding such a fixed point on the $k$-dimensional grid of side length $n$ under the $\leq$ relation. Specifically, there is an unknown monotone function $f: \{0,1,\ldots, n-1\}^k \to \{0,1,\ldots, n-1\}^k$ and an algorithm must query a vertex $v$ to learn $f(v)$. A key special case of interest is the Boolean hypercube $\{0,1\}^k$, which is isomorphic to the power set lattice -- the original setting of the Knaster-Tarski theorem. Our lower bound characterizes the randomized and deterministic query complexity of the Tarski search problem on the Boolean hypercube as $\Theta(k)$. More generally, we prove a randomized lower bound of $\Omega\left( k + \frac{k \cdot \log{n}}{\log{k}} \right)$ for the $k$-dimensional grid of side length $n$, which is asymptotically tight in high dimensions when $k$ is large relative to $n$.