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Assistive devices, such as exoskeletons and prostheses, have revolutionized the field of rehabilitation and mobility assistance. Efficiently detecting transitions between different activities, such as walking, stair ascending and descending, and sitting, is crucial for ensuring adaptive control and enhancing user experience. We here present an approach for real-time transition detection, aimed at optimizing the processing-time performance. By establishing activity-specific threshold values through trained machine learning models, we effectively distinguish motion patterns and we identify transition moments between locomotion modes. This threshold-based method improves real-time embedded processing time performance by up to 11 times compared to machine learning approaches. The efficacy of the developed finite-state machine is validated using data collected from three different measurement systems. Moreover, experiments with healthy participants were conducted on an active pelvis orthosis to validate the robustness and reliability of our approach. The proposed algorithm achieved high accuracy in detecting transitions between activities. These promising results show the robustness and reliability of the method, reinforcing its potential for integration into practical applications.

Nested Sampling is a method for computing the Bayesian evidence, also called the marginal likelihood, which is the integral of the likelihood with respect to the prior. More generally, it is a numerical probabilistic quadrature rule. The main idea of Nested Sampling is to replace a high-dimensional likelihood integral over parameter space with an integral over the unit line by employing a push-forward with respect to a suitable transformation. Practically, a set of active samples ascends the level sets of the integrand function, with the measure contraction of the super-level sets being statistically estimated. We justify the validity of this approach for integrands with non-negligible plateaus, and demonstrate Nested Sampling's practical effectiveness in estimating the (log-)probability of rare events.

Many neural networks deployed in the real world scenarios are trained using cross entropy based loss functions. From the optimization perspective, it is known that the behavior of first order methods such as gradient descent crucially depend on the separability of datasets. In fact, even in the most simplest case of binary classification, the rate of convergence depends on two factors: (1) condition number of data matrix, and (2) separability of the dataset. With no further pre-processing techniques such as over-parametrization, data augmentation etc., separability is an intrinsic quantity of the data distribution under consideration. We focus on the landscape design of the logistic function and derive a novel sequence of {\em strictly} convex functions that are at least as strict as logistic loss. The minimizers of these functions coincide with those of the minimum norm solution wherever possible. The strict convexity of the derived function can be extended to finetune state-of-the-art models and applications. In empirical experimental analysis, we apply our proposed rooted logistic objective to multiple deep models, e.g., fully-connected neural networks and transformers, on various of classification benchmarks. Our results illustrate that training with rooted loss function is converged faster and gains performance improvements. Furthermore, we illustrate applications of our novel rooted loss function in generative modeling based downstream applications, such as finetuning StyleGAN model with the rooted loss. The code implementing our losses and models can be found here for open source software development purposes: //anonymous.4open.science/r/rooted_loss.

Variational dimensionality reduction methods are known for their high accuracy, generative abilities, and robustness. These methods have many theoretical justifications. Here we introduce a unifying principle rooted in information theory to rederive and generalize existing variational methods and design new ones. We base our framework on an interpretation of the multivariate information bottleneck, in which two Bayesian networks are traded off against one another. We interpret the first network as an encoder graph, which specifies what information to keep when compressing the data. We interpret the second network as a decoder graph, which specifies a generative model for the data. Using this framework, we rederive existing dimensionality reduction methods such as the deep variational information bottleneck (DVIB), beta variational auto-encoders (beta-VAE), and deep variational canonical correlation analysis (DVCCA). The framework naturally introduces a trade-off parameter between compression and reconstruction in the DVCCA family of algorithms, resulting in the new beta-DVCCA family. In addition, we derive a new variational dimensionality reduction method, deep variational symmetric informational bottleneck (DVSIB), which simultaneously compresses two variables to preserve information between their compressed representations. We implement all of these algorithms and evaluate their ability to produce shared low dimensional latent spaces on a modified noisy MNIST dataset. We show that algorithms that are better matched to the structure of the data (beta-DVCCA and DVSIB) produce better latent spaces as measured by classification accuracy and the dimensionality of the latent variables. We believe that this framework can be used to unify other multi-view representation learning algorithms. Additionally, it provides a straightforward framework for deriving problem-specific loss functions.

Non-compliance is common in real world experiments. We focus on inference about the sample complier average causal effect, that is, the average treatment effect for experimental units who are compliers. We present three types of inference strategies for the sample complier average causal effect: the Wald estimator, regression adjustment estimators and model-based Bayesian inference. Because modern computer assisted experimental designs have been used to improve covariate balance over complete randomization, we discuss inference under both complete randomization and a specific computer assisted experimental design - Mahalanobis distance based rerandomization, under which asymptotic properties of the Wald estimator and regression adjustment estimators can be derived. We use Monte Carlo simulation to compare the finite sample performance of the methods under both experimental designs. We find that under either design, the Bayesian method performs the best because it is stable, it yields smallest median absolute error and smallest median interval length. The improvement by the Bayesian method is especially large when the fraction of compliers is small. We present an application to a job training experiment with non-compliance.

The optimal rate at which information can be sent through a quantum channel when the transmitted signal must simultaneously carry some minimum amount of energy is characterized. To do so, we introduce the quantum-classical analogue of the capacity-power function and generalize results in classical information theory for transmitting classical information through noisy channels. We show that the capacity-power function for a quantum channel, for both unassisted and private protocol, is concave and also prove additivity for unentangled and uncorrelated ensembles of input signals. This implies we do not need regularized formulas for calculation. We numerically demonstrate these properties for some standard channel models. We obtain analytical expressions for the capacity-power function for the case of noiseless channels using properties of random quantum states and concentration phenomenon in large Hilbert spaces.

Graph Convolutional Networks (GCNs) have been widely applied in various fields due to their significant power on processing graph-structured data. Typical GCN and its variants work under a homophily assumption (i.e., nodes with same class are prone to connect to each other), while ignoring the heterophily which exists in many real-world networks (i.e., nodes with different classes tend to form edges). Existing methods deal with heterophily by mainly aggregating higher-order neighborhoods or combing the immediate representations, which leads to noise and irrelevant information in the result. But these methods did not change the propagation mechanism which works under homophily assumption (that is a fundamental part of GCNs). This makes it difficult to distinguish the representation of nodes from different classes. To address this problem, in this paper we design a novel propagation mechanism, which can automatically change the propagation and aggregation process according to homophily or heterophily between node pairs. To adaptively learn the propagation process, we introduce two measurements of homophily degree between node pairs, which is learned based on topological and attribute information, respectively. Then we incorporate the learnable homophily degree into the graph convolution framework, which is trained in an end-to-end schema, enabling it to go beyond the assumption of homophily. More importantly, we theoretically prove that our model can constrain the similarity of representations between nodes according to their homophily degree. Experiments on seven real-world datasets demonstrate that this new approach outperforms the state-of-the-art methods under heterophily or low homophily, and gains competitive performance under homophily.

Few-shot Knowledge Graph (KG) completion is a focus of current research, where each task aims at querying unseen facts of a relation given its few-shot reference entity pairs. Recent attempts solve this problem by learning static representations of entities and references, ignoring their dynamic properties, i.e., entities may exhibit diverse roles within task relations, and references may make different contributions to queries. This work proposes an adaptive attentional network for few-shot KG completion by learning adaptive entity and reference representations. Specifically, entities are modeled by an adaptive neighbor encoder to discern their task-oriented roles, while references are modeled by an adaptive query-aware aggregator to differentiate their contributions. Through the attention mechanism, both entities and references can capture their fine-grained semantic meanings, and thus render more expressive representations. This will be more predictive for knowledge acquisition in the few-shot scenario. Evaluation in link prediction on two public datasets shows that our approach achieves new state-of-the-art results with different few-shot sizes.

Knowledge graph completion aims to predict missing relations between entities in a knowledge graph. While many different methods have been proposed, there is a lack of a unifying framework that would lead to state-of-the-art results. Here we develop PathCon, a knowledge graph completion method that harnesses four novel insights to outperform existing methods. PathCon predicts relations between a pair of entities by: (1) Considering the Relational Context of each entity by capturing the relation types adjacent to the entity and modeled through a novel edge-based message passing scheme; (2) Considering the Relational Paths capturing all paths between the two entities; And, (3) adaptively integrating the Relational Context and Relational Path through a learnable attention mechanism. Importantly, (4) in contrast to conventional node-based representations, PathCon represents context and path only using the relation types, which makes it applicable in an inductive setting. Experimental results on knowledge graph benchmarks as well as our newly proposed dataset show that PathCon outperforms state-of-the-art knowledge graph completion methods by a large margin. Finally, PathCon is able to provide interpretable explanations by identifying relations that provide the context and paths that are important for a given predicted relation.

Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis, thereby allowing manual manipulation in predicting the final answer.