Multivariate data having both continuous and discrete variables is known as mixed outcomes and has widely appeared in a variety of fields such as ecology, epidemiology, and climatology. In order to understand the probability structure of multivariate data, the estimation of the dependence structure among mixed outcomes is very important. However, when location information is equipped with multivariate data, the spatial correlation should be adequately taken into account; otherwise, the estimation of the dependence structure would be severely biased. To solve this issue, we propose a semiparametric Bayesian inference for the dependence structure among mixed outcomes while eliminating spatial correlation. To this end, we consider a hierarchical spatial model based on the rank likelihood and a latent multivariate Gaussian process. We develop an efficient algorithm for computing the posterior using the Markov Chain Monte Carlo. We also provide a scalable implementation of the model using the nearest-neighbor Gaussian process under large spatial datasets. We conduct a simulation study to validate our proposed procedure and demonstrate that the procedure successfully accounts for spatial correlation and correctly infers the dependence structure among outcomes. Furthermore, the procedure is applied to a real example collected during an international synoptic krill survey in the Scotia Sea of the Antarctic Peninsula, which includes sighting data of fin whales (Balaenoptera physalus), and the relevant oceanographic data.
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Modeling the correlations among errors is closely associated with how accurately the model can quantify predictive uncertainty in probabilistic time series forecasting. Recent multivariate models have made significant progress in accounting for contemporaneous correlations among errors, while a common assumption on these errors is that they are temporally independent for the sake of statistical simplicity. However, real-world observations often deviate from this assumption, since errors usually exhibit substantial autocorrelation due to various factors such as the exclusion of temporally correlated covariates. In this work, we propose an efficient method, based on a low-rank-plus-diagonal parameterization of the covariance matrix, which can effectively characterize the autocorrelation of errors. The proposed method possesses several desirable properties: the complexity does not scale with the number of time series, the resulting covariance can be used for calibrating predictions, and it can seamlessly integrate with any model with Gaussian-distributed errors. We empirically demonstrate these properties using two distinct neural forecasting models-GPVar and Transformer. Our experimental results confirm the effectiveness of our method in enhancing predictive accuracy and the quality of uncertainty quantification on multiple real-world datasets.
The probabilistic formal verification (PFV) of AI systems is in its infancy. So far, approaches have been limited to ad-hoc algorithms for specific classes of models and/or properties. We propose a unifying framework for the PFV of AI systems based onWeighted Model Integration (WMI), which allows to frame the problem in very general terms. Crucially, this reduction enables the verification of many properties of interest, like fairness, robustness or monotonicity, over a wide range of machine learning models, without making strong distributional assumptions. We support the generality of the approach by solving multiple verification tasks with a single, off-the-shelf WMI solver, then discuss the scalability challenges and research directions related to this promising framework.
Current validation methods often rely on recorded data and basic functional checks, which may not be sufficient to encompass the scenarios an autonomous vehicle might encounter. In addition, there is a growing need for complex scenarios with changing vehicle interactions for comprehensive validation. This work introduces a novel synchronous multi-agent simulation framework for autonomous vehicles in interactive scenarios. Our approach creates an interactive scenario and incorporates publicly available edge-case scenarios wherein simulated vehicles are replaced by agents navigating to predefined destinations. We provide a platform that enables the integration of different autonomous driving planning methodologies and includes a set of evaluation metrics to assess autonomous driving behavior. Our study explores different planning setups and adjusts simulation complexity to test the framework's adaptability and performance. Results highlight the critical role of simulating vehicle interactions to enhance autonomous driving systems. Our setup offers unique insights for developing advanced algorithms for complex driving tasks to accelerate future investigations and developments in this field. The multi-agent simulation framework is available as open-source software: //github.com/TUM-AVS/Frenetix-Motion-Planner
Sheaves are mathematical objects consisting of a base which constitutes a topological space and the data associated with each open set thereof, e.g. continuous functions defined on the open sets. Sheaves have originally been used in algebraic topology and logic. Recently, they have also modelled events such as physical experiments and natural language disambiguation processes. We extend the latter models from lexical ambiguities to discourse ambiguities arising from anaphora. To begin, we calculated a new measure of contextuality for a dataset of basic anaphoric discourses, resulting in a higher proportion of contextual models--82.9%--compared to previous work which only yielded 3.17% contextual models. Then, we show how an extension of the natural language processing challenge, known as the Winograd Schema, which involves anaphoric ambiguities can be modelled on the Bell-CHSH scenario with a contextual fraction of 0.096.
Large language models (LLMs) have significantly advanced the field of natural language processing (NLP), providing a highly useful, task-agnostic foundation for a wide range of applications. The great promise of LLMs as general task solvers motivated people to extend their functionality largely beyond just a ``chatbot'', and use it as an assistant or even replacement for domain experts and tools in specific domains such as healthcare, finance, and education. However, directly applying LLMs to solve sophisticated problems in specific domains meets many hurdles, caused by the heterogeneity of domain data, the sophistication of domain knowledge, the uniqueness of domain objectives, and the diversity of the constraints (e.g., various social norms, cultural conformity, religious beliefs, and ethical standards in the domain applications). To fill such a gap, explosively-increase research, and practices have been conducted in very recent years on the domain specialization of LLMs, which, however, calls for a comprehensive and systematic review to better summarizes and guide this promising domain. In this survey paper, first, we propose a systematic taxonomy that categorizes the LLM domain-specialization techniques based on the accessibility to LLMs and summarizes the framework for all the subcategories as well as their relations and differences to each other. We also present a comprehensive taxonomy of critical application domains that can benefit from specialized LLMs, discussing their practical significance and open challenges. Furthermore, we offer insights into the current research status and future trends in this area.
The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.
As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.
Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.
With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.
While it is nearly effortless for humans to quickly assess the perceptual similarity between two images, the underlying processes are thought to be quite complex. Despite this, the most widely used perceptual metrics today, such as PSNR and SSIM, are simple, shallow functions, and fail to account for many nuances of human perception. Recently, the deep learning community has found that features of the VGG network trained on the ImageNet classification task has been remarkably useful as a training loss for image synthesis. But how perceptual are these so-called "perceptual losses"? What elements are critical for their success? To answer these questions, we introduce a new Full Reference Image Quality Assessment (FR-IQA) dataset of perceptual human judgments, orders of magnitude larger than previous datasets. We systematically evaluate deep features across different architectures and tasks and compare them with classic metrics. We find that deep features outperform all previous metrics by huge margins. More surprisingly, this result is not restricted to ImageNet-trained VGG features, but holds across different deep architectures and levels of supervision (supervised, self-supervised, or even unsupervised). Our results suggest that perceptual similarity is an emergent property shared across deep visual representations.
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