The conditional mutual information quantifies the conditional dependence of two random variables. It has numerous applications; it forms, for example, part of the definition of transfer entropy, a common measure of the causal relationship between time series. It does, however, require a lot of data to estimate accurately and suffers the curse of dimensionality, limiting its application in machine learning and data science. However, the Kozachenko-Leonenko approach can address this problem: it is possible, in this approach to define a nearest-neighbour estimator which depends only on the distance between data points and not on the dimension of the data. Furthermore, the bias can be calculated analytically for this estimator. Here this estimator is described and is tested on simulated data.
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The fusion of hyperspectral and LiDAR data has been an active research topic. Existing fusion methods have ignored the high-dimensionality and redundancy challenges in hyperspectral images, despite that band selection methods have been intensively studied for hyperspectral image (HSI) processing. This paper addresses this significant gap by introducing a cross-attention mechanism from the transformer architecture for the selection of HSI bands guided by LiDAR data. LiDAR provides high-resolution vertical structural information, which can be useful in distinguishing different types of land cover that may have similar spectral signatures but different structural profiles. In our approach, the LiDAR data are used as the "query" to search and identify the "key" from the HSI to choose the most pertinent bands for LiDAR. This method ensures that the selected HSI bands drastically reduce redundancy and computational requirements while working optimally with the LiDAR data. Extensive experiments have been undertaken on three paired HSI and LiDAR data sets: Houston 2013, Trento and MUUFL. The results highlight the superiority of the cross-attention mechanism, underlining the enhanced classification accuracy of the identified HSI bands when fused with the LiDAR features. The results also show that the use of fewer bands combined with LiDAR surpasses the performance of state-of-the-art fusion models.
While density functional theory (DFT) serves as a prevalent computational approach in electronic structure calculations, its computational demands and scalability limitations persist. Recently, leveraging neural networks to parameterize the Kohn-Sham DFT Hamiltonian has emerged as a promising avenue for accelerating electronic structure computations. Despite advancements, challenges such as the necessity for computing extensive DFT training data to explore each new system and the complexity of establishing accurate ML models for multi-elemental materials still exist. Addressing these hurdles, this study introduces a universal electronic Hamiltonian model trained on Hamiltonian matrices obtained from first-principles DFT calculations of nearly all crystal structures on the Materials Project. We demonstrate its generality in predicting electronic structures across the whole periodic table, including complex multi-elemental systems, solid-state electrolytes, Moir\'e twisted bilayer heterostructure, and metal-organic frameworks (MOFs). Moreover, we utilize the universal model to conduct high-throughput calculations of electronic structures for crystals in GeNOME datasets, identifying 3,940 crystals with direct band gaps and 5,109 crystals with flat bands. By offering a reliable efficient framework for computing electronic properties, this universal Hamiltonian model lays the groundwork for advancements in diverse fields, such as easily providing a huge data set of electronic structures and also making the materials design across the whole periodic table possible.
By deploying a large number of antennas with sub-half-wavelength spacing in a compact space, dense array systems(DASs) can fully unleash the multiplexing-and-diversity gains of limited apertures. To acquire these gains, accurate channel state information acquisition is necessary but challenging due to the large antenna numbers. To overcome this obstacle, this paper reveals that exploiting the high spatial correlation of DAS channels is crucial while designing the observation matrix for optimal/near-optimal channel estimation. Firstly, we prove that the observation matrix design is equivalent to a time-domain duality of multiple-input multiple-output precoding, which can be ideally addressed by the water-filling principle. For practical realizations, a novel ice-filling algorithm is proposed to design amplitude-and-phase controllable observation matrices, and a majorization-minimization algorithm is proposed to address the phase-only controllable case. Particularly, we prove that the ice-filling algorithm can be viewed as a ``quantized" water-filling algorithm. To support the sub-optimality of the proposed designs, we provide comprehensive analyses on the achievable mean square errors and their asymptotic expressions. Finally, numerical simulations verify that our proposed channel estimation designs can achieve the near-optimal performance and outperform existing approaches significantly.
Unobserved confounding is common in many applications, making causal inference from observational data challenging. As a remedy, causal sensitivity analysis is an important tool to draw causal conclusions under unobserved confounding with mathematical guarantees. In this paper, we propose NeuralCSA, a neural framework for generalized causal sensitivity analysis. Unlike previous work, our framework is compatible with (i) a large class of sensitivity models, including the marginal sensitivity model, f-sensitivity models, and Rosenbaum's sensitivity model; (ii) different treatment types (i.e., binary and continuous); and (iii) different causal queries, including (conditional) average treatment effects and simultaneous effects on multiple outcomes. The generality of NeuralCSA is achieved by learning a latent distribution shift that corresponds to a treatment intervention using two conditional normalizing flows. We provide theoretical guarantees that NeuralCSA is able to infer valid bounds on the causal query of interest and also demonstrate this empirically using both simulated and real-world data.
We propose a new continuous phase frequency shift keying that is particularly suited for multi-antenna communications when the link budget is critical and beam alignment is problematic. It combines the constant envelope of frequency modulation with low-rate repetition coding in order to compensate for the absence of transmit beamforming. Although it is a frequency modulation, its transmit signal shows close to rectangular spectral shape. Similar to GSM's Gaussian minimum shift keying, it can be well approximated by linear modulation, when combined with differential precoding. This allows for easy coherent demodulation by means of a windowed fast Fourier transform.
The conventional wisdom of manifold learning is based on nonlinear dimensionality reduction techniques such as IsoMAP and locally linear embedding (LLE). We challenge this paradigm by exploiting the blessing of dimensionality. Our intuition is simple: it is easier to untangle a low-dimensional manifold in a higher-dimensional space due to its vastness, as guaranteed by Whitney embedding theorem. A new insight brought by this work is to introduce class labels as the context variables in the lifted higher-dimensional space (so supervised learning becomes unsupervised learning). We rigorously show that manifold untangling leads to linearly separable classifiers in the lifted space. To correct the inevitable overfitting, we consider the dual process of manifold untangling -- tangling or aliasing -- which is important for generalization. Using context as the bonding element, we construct a pair of manifold untangling and tangling operators, known as tangling-untangling cycle (TUC). Untangling operator maps context-independent representations (CIR) in low-dimensional space to context-dependent representations (CDR) in high-dimensional space by inducing context as hidden variables. The tangling operator maps CDR back to CIR by a simple integral transformation for invariance and generalization. We also present the hierarchical extensions of TUC based on the Cartesian product and the fractal geometry. Despite the conceptual simplicity, TUC admits a biologically plausible and energy-efficient implementation based on the time-locking behavior of polychronization neural groups (PNG) and sleep-wake cycle (SWC). The TUC-based theory applies to the computational modeling of various cognitive functions by hippocampal-neocortical systems.
Entity Resolution (ER) is the problem of semi-automatically determining when two entities refer to the same underlying entity, with applications ranging from healthcare to e-commerce. Traditional ER solutions required considerable manual expertise, including domain-specific feature engineering, as well as identification and curation of training data. Recently released large language models (LLMs) provide an opportunity to make ER more seamless and domain-independent. However, it is also well known that LLMs can pose risks, and that the quality of their outputs can depend on how prompts are engineered. Unfortunately, a systematic experimental study on the effects of different prompting methods for addressing unsupervised ER, using LLMs like ChatGPT, has been lacking thus far. This paper aims to address this gap by conducting such a study. We consider some relatively simple and cost-efficient ER prompt engineering methods and apply them to ER on two real-world datasets widely used in the community. We use an extensive set of experimental results to show that an LLM like GPT3.5 is viable for high-performing unsupervised ER, and interestingly, that more complicated and detailed (and hence, expensive) prompting methods do not necessarily outperform simpler approaches. We provide brief discussions on qualitative and error analysis, including a study of the inter-consistency of different prompting methods to determine whether they yield stable outputs. Finally, we consider some limitations of LLMs when applied to ER.
Gaussian smoothed sliced Wasserstein distance has been recently introduced for comparing probability distributions, while preserving privacy on the data. It has been shown that it provides performances similar to its non-smoothed (non-private) counterpart. However, the computationaland statistical properties of such a metric have not yet been well-established. This work investigates the theoretical properties of this distance as well as those of generalized versions denoted as Gaussian-smoothed sliced divergences. We first show that smoothing and slicing preserve the metric property and the weak topology. To study the sample complexity of such divergences, we then introduce $\hat{\hat\mu}_{n}$ the double empirical distribution for the smoothed-projected $\mu$. The distribution $\hat{\hat\mu}_{n}$ is a result of a double sampling process: one from sampling according to the origin distribution $\mu$ and the second according to the convolution of the projection of $\mu$ on the unit sphere and the Gaussian smoothing. We particularly focus on the Gaussian smoothed sliced Wasserstein distance and prove that it converges with a rate $O(n^{-1/2})$. We also derive other properties, including continuity, of different divergences with respect to the smoothing parameter. We support our theoretical findings with empirical studies in the context of privacy-preserving domain adaptation.
Existing prompt learning methods have shown certain capabilities in Out-of-Distribution (OOD) detection, but the lack of OOD images in the target dataset in their training can lead to mismatches between OOD images and In-Distribution (ID) categories, resulting in a high false positive rate. To address this issue, we introduce a novel OOD detection method, named 'NegPrompt', to learn a set of negative prompts, each representing a negative connotation of a given class label, for delineating the boundaries between ID and OOD images. It learns such negative prompts with ID data only, without any reliance on external outlier data. Further, current methods assume the availability of samples of all ID classes, rendering them ineffective in open-vocabulary learning scenarios where the inference stage can contain novel ID classes not present during training. In contrast, our learned negative prompts are transferable to novel class labels. Experiments on various ImageNet benchmarks show that NegPrompt surpasses state-of-the-art prompt-learning-based OOD detection methods and maintains a consistent lead in hard OOD detection in closed- and open-vocabulary classification scenarios. Code is available at //github.com/mala-lab/negprompt.
The Internet of Things (IoT) is a communication scheme which allows various objects to exchange several types of information, enabling functions such as home automation, production management, healthcare, etc. Moreover, energy-harvesting (EH) technology is considered for IoT environment in order to reduce the need for management and enhance maintainability. However, since environments considering outdoor elements such as pedestrians, vehicles and drones have been on the rise recently, it is important to consider mobility when designing an IoT network management scheme. In order to handle this challenge, prior research has made an attempt to solve this problem via variational autoencoder (VAE) and backward-pass rate evaluation method. In this article, we propose a guided-mutation genetic algorithm (GMGA) to derive a sub-optimal relaying topology for IoT systems considering energy-harvesting. Furthermore, we propose a mobility-aware iterative relaying topology algorithm, which calculates the sub-optimal relaying topology of current time frame using the topology result of the previous one. Simulation results verify that our proposed scheme effectively solves formulated IoT network problems compared to other conventional schemes, and also effectively handles IoT environments in terms of mobility.
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