We establish finite-sample guarantees for efficient proper learning of bounded-degree polytrees, a rich class of high-dimensional probability distributions and a subclass of Bayesian networks, a widely-studied type of graphical model. Recently, Bhattacharyya et al. (2021) obtained finite-sample guarantees for recovering tree-structured Bayesian networks, i.e., 1-polytrees. We extend their results by providing an efficient algorithm which learns $d$-polytrees in polynomial time and sample complexity for any bounded $d$ when the underlying undirected graph (skeleton) is known. We complement our algorithm with an information-theoretic sample complexity lower bound, showing that the dependence on the dimension and target accuracy parameters are nearly tight.
Support vector machines (SVMs) are widely used and constitute one of the best examined and used machine learning models for two-class classification. Classification in SVM is based on a score procedure, yielding a deterministic classification rule, which can be transformed into a probabilistic rule (as implemented in off-the-shelf SVM libraries), but is not probabilistic in nature. On the other hand, the tuning of the regularization parameters in SVM is known to imply a high computational effort and generates pieces of information that are not fully exploited, not being used to build a probabilistic classification rule. In this paper we propose a novel approach to generate probabilistic outputs for the SVM. The new method has the following three properties. First, it is designed to be cost-sensitive, and thus the different importance of sensitivity (or true positive rate, TPR) and specificity (true negative rate, TNR) is readily accommodated in the model. As a result, the model can deal with imbalanced datasets which are common in operational business problems as churn prediction or credit scoring. Second, the SVM is embedded in an ensemble method to improve its performance, making use of the valuable information generated in the parameters tuning process. Finally, the probabilities estimation is done via bootstrap estimates, avoiding the use of parametric models as competing approaches. Numerical tests on a wide range of datasets show the advantages of our approach over benchmark procedures.
Infrared small target detection plays an important role in the remote sensing fields. Therefore, many detection algorithms have been proposed, in which the infrared patch-tensor (IPT) model has become a mainstream tool due to its excellent performance. However, most IPT-based methods face great challenges, such as inaccurate measure of the tensor low-rankness and poor robustness to complex scenes, which will leadto poor detection performance. In order to solve these problems, this paper proposes a novel double-weighted multi-granularity infrared patch tensor (DWMGIPT) model. First, to capture different granularity information of tensor from multiple modes, a multi-granularity infrared patch tensor (MGIPT) model is constructed by collecting nonoverlapping patches and tensor augmentation based on the tensor train (TT) decomposition. Second, to explore the latent structure of tensor more efficiently, we utilize the auto-weighted mechanism to balance the importance of information at different granularity. Then, the steering kernel (SK) is employed to extract local structure prior, which suppresses background interference such as strong edges and noise. Finally, an efficient optimization algorithm based on the alternating direction method of multipliers (ADMM) is presented to solve the model. Extensive experiments in various challenging scenes show that the proposed algorithm is robust to noise and different scenes. Compared with the other eight state-of-the-art methods, different evaluation metrics demonstrate that our method achieves better detection performance in various complex scenes.
Property prediction on molecular graphs is an important application of Graph Neural Networks (GNNs). Recently, unlabeled molecular data has become abundant, which facilitates the rapid development of self-supervised learning for GNNs in the chemical domain. In this work, we propose pretraining GNNs at the fragment level, which serves as a promising middle ground to overcome the limitations of node-level and graph-level pretraining. Borrowing techniques from recent work on principle subgraph mining, we obtain a compact vocabulary of prevalent fragments that span a large pretraining dataset. From the extracted vocabulary, we introduce several fragment-based contrastive and predictive pretraining tasks. The contrastive learning task jointly pretrains two different GNNs: one based on molecular graphs and one based on fragment graphs, which represents high-order connectivity within molecules. By enforcing the consistency between the fragment embedding and the aggregated embedding of the corresponding atoms from the molecular graphs, we ensure that both embeddings capture structural information at multiple resolutions. The structural information of the fragment graphs is further exploited to extract auxiliary labels for the graph-level predictive pretraining. We employ both the pretrained molecular-based and fragment-based GNNs for downstream prediction, thus utilizing the fragment information during finetuning. Our models advance the performances on 5 out of 8 common molecular benchmarks and improve the performances on long-range biological benchmarks by at least 11.5%.
Visual language reasoning requires a system to extract text or numbers from information-dense images like charts or plots and perform logical or arithmetic reasoning to arrive at an answer. To tackle this task, existing work relies on either (1) an end-to-end vision-language model trained on a large amount of data, or (2) a two-stage pipeline where a captioning model converts the image into text that is further read by another large language model to deduce the answer. However, the former approach forces the model to answer a complex question with one single step, and the latter approach is prone to inaccurate or distracting information in the converted text that can confuse the language model. In this work, we propose a dual-system for multi-step multimodal reasoning, which consists of a "System-1" step for visual information extraction and a "System-2" step for deliberate reasoning. Given an input, System-2 breaks down the question into atomic sub-steps, each guiding System-1 to extract the information required for reasoning from the image. Experiments on chart and plot datasets show that our method with a pre-trained System-2 module performs competitively compared to prior work on in- and out-of-distribution data. By fine-tuning the System-2 module (LLaMA-2 70B) on only a small amount of data on multi-step reasoning, the accuracy of our method is further improved and surpasses the best fully-supervised end-to-end approach by 5.7% and a pipeline approach with FlanPaLM (540B) by 7.5% on a challenging dataset with human-authored questions.
In the intricate architecture of the mammalian central nervous system, neurons form populations. Axonal bundles communicate between these clusters using spike trains as their medium. However, these neuron populations' precise encoding and operations have yet to be discovered. In our analysis, the starting point is a state-of-the-art mechanistic model of a generic neuron endowed with plasticity. From this simple framework emerges a profound mathematical construct: The representation and manipulation of information can be precisely characterized by an algebra of finite convex cones. Furthermore, these neuron populations are not merely passive transmitters. They act as operators within this algebraic structure, mirroring the functionality of a low-level programming language. When these populations interconnect, they embody succinct yet potent algebraic expressions. These networks allow them to implement many operations, such as specialization, generalization, novelty detection, dimensionality reduction, inverse modeling, prediction, and associative memory. In broader terms, this work illuminates the potential of matrix embeddings in advancing our understanding in fields like cognitive science and AI. These embeddings enhance the capacity for concept processing and hierarchical description over their vector counterparts.
A good representation of a large, complex mobile robot workspace must be space-efficient yet capable of encoding relevant geometric details. When exploring unknown environments, it needs to be updatable incrementally in an online fashion. We introduce HIO-SDF, a new method that represents the environment as a Signed Distance Field (SDF). State of the art representations of SDFs are based on either neural networks or voxel grids. Neural networks are capable of representing the SDF continuously. However, they are hard to update incrementally as neural networks tend to forget previously observed parts of the environment unless an extensive sensor history is stored for training. Voxel-based representations do not have this problem but they are not space-efficient especially in large environments with fine details. HIO-SDF combines the advantages of these representations using a hierarchical approach which employs a coarse voxel grid that captures the observed parts of the environment together with high-resolution local information to train a neural network. HIO-SDF achieves a 46% lower mean global SDF error across all test scenes than a state of the art continuous representation, and a 30% lower error than a discrete representation at the same resolution as our coarse global SDF grid.
The death toll and monetary damages from landslides continue to rise despite advancements in predictive modeling. The predictive capability of these models is limited as landslide databases used in training and assessing the models often have crucial information missing, such as underlying failure types. Here, we present an approach for identifying failure types based on their movements, e.g., slides and flows by leveraging 3D landslide topology. We observe topological proxies reveal prevalent signatures of mass movement mechanics embedded in the landslide's morphology or shape, such as detecting coupled movement styles within complex landslides. We find identical failure types exhibit similar topological properties, and by using them as predictors, we can identify failure types in historic and event-specific landslide databases (including multi-temporal) from various geomorphological and climatic contexts such as Italy, the US Pacific Northwest region, Denmark, Turkey, and China with 80 to 94 % accuracy. To demonstrate the real-world application of the method, we implement it in two undocumented datasets from China and publicly release the datasets. These new insights can considerably improve the performance of landslide predictive models and impact assessments. Moreover, our work introduces a new paradigm for studying landslide shapes to understand underlying processes through the lens of landslide topology.
This paper focuses on a novel approach for detecting moving objects during camera motion. We present an optical-flow-based transformation that yields a consistent 2D invariant image output regardless of time instants, range of points in 3D, and the speed of the camera. In other words, this transformation generates a lookup image that remains invariant despite the changing projection of the 3D scene and camera motion. In the new domain, projections of 3D points that deviate from the values of the predefined lookup image can be clearly identified as moving relative to the stationary 3D environment, making them seamlessly detectable. The method does not require prior knowledge of the direction of motion or speed of the camera, nor does it necessitate 3D point range information. It is well-suited for real-time parallel processing, rendering it highly practical for implementation. We have validated the effectiveness of the new domain through simulations and experiments, demonstrating its robustness in scenarios involving rectilinear camera motion, both in simulations and with real-world data. This approach introduces new ways for moving objects detection during camera motion, and also lays the foundation for future research in the context of moving object detection during six-degrees-of-freedom camera motion.
Test-Time Adaptation (TTA) is a critical paradigm for tackling distribution shifts during inference, especially in visual recognition tasks. However, while acoustic models face similar challenges due to distribution shifts in test-time speech, TTA techniques specifically designed for acoustic modeling in the context of open-world data shifts remain scarce. This gap is further exacerbated when considering the unique characteristics of acoustic foundation models: 1) they are primarily built on transformer architectures with layer normalization and 2) they deal with test-time speech data of varying lengths in a non-stationary manner. These aspects make the direct application of vision-focused TTA methods, which are mostly reliant on batch normalization and assume independent samples, infeasible. In this paper, we delve into TTA for pre-trained acoustic models facing open-world data shifts. We find that noisy, high-entropy speech frames, often non-silent, carry key semantic content. Traditional TTA methods might inadvertently filter out this information using potentially flawed heuristics. In response, we introduce a heuristic-free, learning-based adaptation enriched by confidence enhancement. Noting that speech signals' short-term consistency, we also apply consistency regularization during test-time optimization. Our experiments on synthetic and real-world datasets affirm our method's superiority over existing baselines.