In this work, we propose a new clustering algorithm to group nodes in networks based on second-order simplices (aka filled triangles) to leverage higher-order network interactions. We define a simplicial conductance function, which on minimizing, yields an optimal partition with a higher density of filled triangles within the set while the density of filled triangles is smaller across the sets. To this end, we propose a simplicial adjacency operator that captures the relation between the nodes through second-order simplices. This allows us to extend the well-known Cheeger inequality to cluster a simplicial complex. Then, leveraging the Cheeger inequality, we propose the simplicial spectral clustering algorithm. We report results from numerical experiments on synthetic and real-world network data to demonstrate the efficacy of the proposed approach.

One of the main motivations of studying continual learning is that the problem setting allows a model to accrue knowledge from past tasks to learn new tasks more efficiently. However, recent studies suggest that the key metric that continual learning algorithms optimize, reduction in catastrophic forgetting, does not correlate well with the forward transfer of knowledge. We believe that the conclusion previous works reached is due to the way they measure forward transfer. We argue that the measure of forward transfer to a task should not be affected by the restrictions placed on the continual learner in order to preserve knowledge of previous tasks. Instead, forward transfer should be measured by how easy it is to learn a new task given a set of representations produced by continual learning on previous tasks. Under this notion of forward transfer, we evaluate different continual learning algorithms on a variety of image classification benchmarks. Our results indicate that less forgetful representations lead to a better forward transfer suggesting a strong correlation between retaining past information and learning efficiency on new tasks. Further, we found less forgetful representations to be more diverse and discriminative compared to their forgetful counterparts.

The Internet of Things (IoT) system generates massive high-speed temporally correlated streaming data and is often connected with online inference tasks under computational or energy constraints. Online analysis of these streaming time series data often faces a trade-off between statistical efficiency and computational cost. One important approach to balance this trade-off is sampling, where only a small portion of the sample is selected for the model fitting and update. Motivated by the demands of dynamic relationship analysis of IoT system, we study the data-dependent sample selection and online inference problem for a multi-dimensional streaming time series, aiming to provide low-cost real-time analysis of high-speed power grid electricity consumption data. Inspired by D-optimality criterion in design of experiments, we propose a class of online data reduction methods that achieve an optimal sampling criterion and improve the computational efficiency of the online analysis. We show that the optimal solution amounts to a strategy that is a mixture of Bernoulli sampling and leverage score sampling. The leverage score sampling involves auxiliary estimations that have a computational advantage over recursive least squares updates. Theoretical properties of the auxiliary estimations involved are also discussed. When applied to European power grid consumption data, the proposed leverage score based sampling methods outperform the benchmark sampling method in online estimation and prediction. The general applicability of the sampling-assisted online estimation method is assessed via simulation studies.

We propose a new method of multiway clustering for 3-order tensors via affinity matrix (MCAM). Based on a notion of similarity between the tensor slices and the spread of information of each slice, our model builds an affinity/similarity matrix on which we apply advanced clustering methods. The combination of all clusters of the three modes delivers the desired multiway clustering. Finally, MCAM achieves competitive results compared with other known algorithms on synthetics and real datasets.

Imitation learning, in which learning is performed by demonstration, has been studied and advanced for sequential decision-making tasks in which a reward function is not predefined. However, imitation learning methods still require numerous expert demonstration samples to successfully imitate an expert's behavior. To improve sample efficiency, we utilize self-supervised representation learning, which can generate vast training signals from the given data. In this study, we propose a self-supervised representation-based adversarial imitation learning method to learn state and action representations that are robust to diverse distortions and temporally predictive, on non-image control tasks. In particular, in comparison with existing self-supervised learning methods for tabular data, we propose a different corruption method for state and action representations that is robust to diverse distortions. We theoretically and empirically observe that making an informative feature manifold with less sample complexity significantly improves the performance of imitation learning. The proposed method shows a 39% relative improvement over existing adversarial imitation learning methods on MuJoCo in a setting limited to 100 expert state-action pairs. Moreover, we conduct comprehensive ablations and additional experiments using demonstrations with varying optimality to provide insights into a range of factors.

Nuclear detection, segmentation and morphometric profiling are essential in helping us further understand the relationship between histology and patient outcome. To drive innovation in this area, we setup a community-wide challenge using the largest available dataset of its kind to assess nuclear segmentation and cellular composition. Our challenge, named CoNIC, stimulated the development of reproducible algorithms for cellular recognition with real-time result inspection on public leaderboards. We conducted an extensive post-challenge analysis based on the top-performing models using 1,658 whole-slide images of colon tissue. With around 700 million detected nuclei per model, associated features were used for dysplasia grading and survival analysis, where we demonstrated that the challenge's improvement over the previous state-of-the-art led to significant boosts in downstream performance. Our findings also suggest that eosinophils and neutrophils play an important role in the tumour microevironment. We release challenge models and WSI-level results to foster the development of further methods for biomarker discovery.

In this paper, we compare three different model-based risk measures by evaluating their stengths and weaknesses qualitatively and testing them quantitatively on a set of real longitudinal and intersection scenarios. We start with the traditional heuristic Time-To-Collision (TTC), which we extend towards 2D operation and non-crash cases to retrieve the Time-To-Closest-Encounter (TTCE). The second risk measure models position uncertainty with a Gaussian distribution and uses spatial occupancy probabilities for collision risks. We then derive a novel risk measure based on the statistics of sparse critical events and so-called survival conditions. The resulting survival analysis shows to have an earlier detection time of crashes and less false positive detections in near-crash and non-crash cases supported by its solid theoretical grounding. It can be seen as a generalization of TTCE and the Gaussian method which is suitable for the validation of ADAS and AD.

Neural-symbolic AI (NeSy) allows neural networks to exploit symbolic background knowledge in the form of logic. It has been shown to aid learning in the limited data regime and to facilitate inference on out-of-distribution data. Probabilistic NeSy focuses on integrating neural networks with both logic and probability theory, which additionally allows learning under uncertainty. A major limitation of current probabilistic NeSy systems, such as DeepProbLog, is their restriction to finite probability distributions, i.e., discrete random variables. In contrast, deep probabilistic programming (DPP) excels in modelling and optimising continuous probability distributions. Hence, we introduce DeepSeaProbLog, a neural probabilistic logic programming language that incorporates DPP techniques into NeSy. Doing so results in the support of inference and learning of both discrete and continuous probability distributions under logical constraints. Our main contributions are 1) the semantics of DeepSeaProbLog and its corresponding inference algorithm, 2) a proven asymptotically unbiased learning algorithm, and 3) a series of experiments that illustrate the versatility of our approach.

We introduce DECAR, a self-supervised pre-training approach for learning general-purpose audio representations. Our system is based on clustering: it utilizes an offline clustering step to provide target labels that act as pseudo-labels for solving a prediction task. We develop on top of recent advances in self-supervised learning for computer vision and design a lightweight, easy-to-use self-supervised pre-training scheme. We pre-train DECAR embeddings on a balanced subset of the large-scale Audioset dataset and transfer those representations to 9 downstream classification tasks, including speech, music, animal sounds, and acoustic scenes. Furthermore, we conduct ablation studies identifying key design choices and also make all our code and pre-trained models publicly available.

Over-parameterized models estimated with some form of gradient descent come in various forms, such as linear regression with potentially non-linear features, neural networks, or kernel methods. The double descent phenomenon can be seen empirically in several of these models [6, 15]: Given a fixed prediction problem, when the number of parameters of the model is increasing from zero to the number of observations, the generalization performance traditionally goes down and then up, due to overfitting. Once the number of parameters exceeds the number of observations, the generalization error decreases again, as illustrated in Figure 1. The phenomenon has been theoretically analyzed in several settings, such as random features based on neural networks [27], random Fourier features [24], or linear regression [7, 17]. While the analysis of [27, 24] for random features corresponds to a single prediction problem with a sequence of increasingly larger prediction models, most of the analysis of [17] for linear regression does not consider a single problem, but varying problems, which does not actually lead to a double descent curve. Random subsampling on a single prediction problem was analyzed with a simpler model with isotropic covariance matrices in [7] and [17, Section 5.2], but without a proper double descent as the model is too simple to account for a U-shaped curve in the under-parameterized regime. In work related to ours, principal component regression was analyzed by [37] with a double descent curve but with less general assumptions regarding the spectrum of the covariance matrix and the optimal predictor.