The development of autonomous vehicles requires having access to a large amount of data in the concerning driving scenarios. However, manual annotation of such driving scenarios is costly and subject to the errors in the rule-based trajectory labeling systems. To address this issue, we propose an effective non-parametric trajectory clustering framework consisting of five stages: (1) aligning trajectories and quantifying their pairwise temporal dissimilarities, (2) embedding the trajectory-based dissimilarities into a vector space, (3) extracting transitive relations, (4) embedding the transitive relations into a new vector space, and (5) clustering the trajectories with an optimal number of clusters. We investigate and evaluate the proposed framework on a challenging real-world dataset consisting of annotated trajectories. We observe that the proposed framework achieves promising results, despite the complexity caused by having trajectories of varying length. Furthermore, we extend the framework to validate the augmentation of the real dataset with synthetic data generated by a Generative Adversarial Network (GAN) where we examine whether the generated trajectories are consistent with the true underlying clusters.

Artificial intelligence nowadays plays an increasingly prominent role in our life since decisions that were once made by humans are now delegated to automated systems. A machine learning algorithm trained based on biased data, however, tends to make unfair predictions. Developing classification algorithms that are fair with respect to protected attributes of the data thus becomes an important problem. Motivated by concerns surrounding the fairness effects of sharing and few-shot machine learning tools, such as the Model Agnostic Meta-Learning framework, we propose a novel fair fast-adapted few-shot meta-learning approach that efficiently mitigates biases during meta-train by ensuring controlling the decision boundary covariance that between the protected variable and the signed distance from the feature vectors to the decision boundary. Through extensive experiments on two real-world image benchmarks over three state-of-the-art meta-learning algorithms, we empirically demonstrate that our proposed approach efficiently mitigates biases on model output and generalizes both accuracy and fairness to unseen tasks with a limited amount of training samples.

In this work we study the stability of algebraic neural networks (AlgNNs) with commutative algebras which unify CNNs and GNNs under the umbrella of algebraic signal processing. An AlgNN is a stacked layered structure where each layer is conformed by an algebra $\mathcal{A}$, a vector space $\mathcal{M}$ and a homomorphism $\rho:\mathcal{A}\rightarrow\text{End}(\mathcal{M})$, where $\text{End}(\mathcal{M})$ is the set of endomorphims of $\mathcal{M}$. Signals in each layer are modeled as elements of $\mathcal{M}$ and are processed by elements of $\text{End}(\mathcal{M})$ defined according to the structure of $\mathcal{A}$ via $\rho$. This framework provides a general scenario that covers several types of neural network architectures where formal convolution operators are being used. We obtain stability conditions regarding to perturbations which are defined as distortions of $\rho$, reaching general results whose particular cases are consistent with recent findings in the literature for CNNs and GNNs. We consider conditions on the domain of the homomorphisms in the algebra that lead to stable operators. Interestingly, we found that these conditions are related to the uniform boundedness of the Fr\'echet derivative of a function $p:\text{End}(\mathcal{M})\rightarrow\text{End}(\mathcal{M})$ that maps the images of the generators of $\mathcal{A}$ on $\text{End}(\mathcal{M})$ into a power series representation that defines the filtering of elements in $\mathcal{M}$. Additionally, our results show that stability is universal to convolutional architectures whose algebraic signal model uses the same algebra.

Comparing metric measure spaces (i.e. a metric space endowed with a probability distribution) is at the heart of many machine learning problems. This includes for instance predicting properties of molecules in quantum chemistry or generating graphs with varying connectivity. The most popular distance between such metric measure spaces is the Gromov-Wasserstein (GW) distance, which is the solution of a quadratic assignment problem. This distance has been successfully applied to supervised learning and generative modeling, for applications as diverse as quantum chemistry or natural language processing. The GW distance is however limited to the comparison of metric measure spaces endowed with a \emph{probability} distribution. This strong limitation is problematic for many applications in ML where there is no a priori natural normalization on the total mass of the data. Furthermore, imposing an exact conservation of mass across spaces is not robust to outliers and often leads to irregular matching. To alleviate these issues, we introduce two Unbalanced Gromov-Wasserstein formulations: a distance and a more computationally tractable upper-bounding relaxation. They both allow the comparison of metric spaces equipped with arbitrary positive measures up to isometries.

RDF2vec is an embedding technique for representing knowledge graph entities in a continuous vector space. In this paper, we investigate the effect of materializing implicit A-box axioms induced by subproperties, as well as symmetric and transitive properties. While it might be a reasonable assumption that such a materialization before computing embeddings might lead to better embeddings, we conduct a set of experiments on DBpedia which demonstrate that the materialization actually has a negative effect on the performance of RDF2vec. In our analysis, we argue that despite the huge body of work devoted on completing missing information in knowledge graphs, such missing implicit information is actually a signal, not a defect, and we show examples illustrating that assumption.

Developing algorithms that are able to generalize to a novel task given only a few labeled examples represents a fundamental challenge in closing the gap between machine- and human-level performance. The core of human cognition lies in the structured, reusable concepts that help us to rapidly adapt to new tasks and provide reasoning behind our decisions. However, existing meta-learning methods learn complex representations across prior labeled tasks without imposing any structure on the learned representations. Here we propose COMET, a meta-learning method that improves generalization ability by learning to learn along human-interpretable concept dimensions. Instead of learning a joint unstructured metric space, COMET learns mappings of high-level concepts into semi-structured metric spaces, and effectively combines the outputs of independent concept learners. We evaluate our model on few-shot tasks from diverse domains, including a benchmark image classification dataset and a novel single-cell dataset from a biological domain developed in our work. COMET significantly outperforms strong meta-learning baselines, achieving $9$-$12\%$ average improvement on the most challenging $1$-shot learning tasks, while unlike existing methods also providing interpretations behind the model's predictions.

In this work, we propose KeRNS: an algorithm for episodic reinforcement learning in non-stationary Markov Decision Processes (MDPs) whose state-action set is endowed with a metric. Using a non-parametric model of the MDP built with time-dependent kernels, we prove a regret bound that scales with the covering dimension of the state-action space and the total variation of the MDP with time, which quantifies its level of non-stationarity. Our method generalizes previous approaches based on sliding windows and exponential discounting used to handle changing environments. We further propose a practical implementation of KeRNS, we analyze its regret and validate it experimentally.

Recently, non-Euclidean spaces became popular for embedding structured data. Following hyperbolic and spherical spaces, more general product spaces have been proposed. However, searching for the best configuration of a product space is a resource-intensive procedure, which reduces the practical applicability of the idea. We introduce a novel concept of overlaying spaces that does not have the problem of configuration search and outperforms the competitors in structured data embedding tasks, when the aim is to preserve all distances. On the other hand, for local loss functions (e.g., for ranking losses), the dot-product similarity, which is often overlooked in graph embedding literature since it cannot be converted to a metric, outperforms all metric spaces. We discuss advantages of the dot product over proper metric spaces.

Metric space magnitude, an active subject of research in algebraic topology, originally arose in the context of biology, where it was used to represent the effective number of distinct species in an environment. In a more general setting, the magnitude of a metric space is a real number that aims to quantify the effective number of distinct points in the space. The contribution of each point to a metric space's global magnitude, which is encoded by the {\em weighting vector}, captures much of the underlying geometry of the original metric space. Surprisingly, when the metric space is Euclidean, the weighting vector also serves as an effective tool for boundary detection. This allows the weighting vector to serve as the foundation of novel algorithms for classic machine learning tasks such as classification, outlier detection and active learning. We demonstrate, using experiments and comparisons on classic benchmark datasets, the promise of the proposed magnitude and weighting vector-based approaches.

Sequence classification is the supervised learning task of building models that predict class labels of unseen sequences of symbols. Although accuracy is paramount, in certain scenarios interpretability is a must. Unfortunately, such trade-off is often hard to achieve since we lack human-independent interpretability metrics. We introduce a novel sequence learning algorithm, that combines (i) linear classifiers - which are known to strike a good balance between predictive power and interpretability, and (ii) background knowledge embeddings. We extend the classic subsequence feature space with groups of symbols which are generated by background knowledge injected via word or graph embeddings, and use this new feature space to learn a linear classifier. We also present a new measure to evaluate the interpretability of a set of symbolic features based on the symbol embeddings. Experiments on human activity recognition from wearables and amino acid sequence classification show that our classification approach preserves predictive power, while delivering more interpretable models.