Time-evolving data sets can often be arranged as a higher-order tensor with one of the modes being the time mode. While tensor factorizations have been successfully used to capture the underlying patterns in such higher-order data sets, the temporal aspect is often ignored, allowing for the reordering of time points. In recent studies, temporal regularizers are incorporated in the time mode to tackle this issue. Nevertheless, existing approaches still do not allow underlying patterns to change in time (e.g., spatial changes in the brain, contextual changes in topics). In this paper, we propose temporal PARAFAC2 (tPARAFAC2): a PARAFAC2-based tensor factorization method with temporal regularization to extract gradually evolving patterns from temporal data. Through extensive experiments on synthetic data, we demonstrate that tPARAFAC2 can capture the underlying evolving patterns accurately performing better than PARAFAC2 and coupled matrix factorization with temporal smoothness regularization.
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Software comprehension can be extremely time-consuming due to the ever-growing size of codebases. Consequently, there is an increasing need to accelerate the code comprehension process to facilitate maintenance and reduce associated costs. A crucial aspect of this process is understanding and preserving the high quality of the code dependency structure. While a variety of code structure models already exist, there is a surprising lack of models that closely represent the source code and focus on software comprehension. As a result, there are no readily available and easy-to-use tools to assist with dependency comprehension, refactoring, and quality monitoring of code. To address this gap, we propose the Semantic Code Graph (SCG), an information model that offers a detailed abstract representation of code dependencies with a close relationship to the source code. To validate the SCG model's usefulness in software comprehension, we compare it to nine other source code representation models. Additionally, we select 11 well-known and widely-used open-source projects developed in Java and Scala and perform a range of software comprehension activities on them using three different code representation models: the proposed SCG, the Call Graph (CG), and the Class Collaboration Network (CCN). We then qualitatively analyze the results to compare the performance of these models in terms of software comprehension capabilities. These activities encompass project structure comprehension, identifying critical project entities, interactive visualization of code dependencies, and uncovering code similarities through software mining. Our findings demonstrate that the SCG enhances software comprehension capabilities compared to the prevailing CCN and CG models. We believe that the work described is a step towards the next generation of tools that streamline code dependency comprehension and management.
Style transfer in DCE-MRI is a challenging task due to large variations in contrast enhancements across different tissues and time. Current unsupervised methods fail due to the wide variety of contrast enhancement and motion between the images in the series. We propose a new method that combines autoencoders to disentangle content and style with convolutional LSTMs to model predicted latent spaces along time and adaptive convolutions to tackle the localised nature of contrast enhancement. To evaluate our method, we propose a new metric that takes into account the contrast enhancement. Qualitative and quantitative analyses show that the proposed method outperforms the state of the art on two different datasets.
The presence of faulty or underactuated manipulators can disrupt the end-effector formation keeping of a team of manipulators. Based on two-link planar manipulators, we investigate this end-effector formation keeping problem for mixed fully- and under-actuated manipulators with flexible joints. In this case, the underactuated manipulators can comprise of active-passive (AP) manipulators, passive-active (PA) manipulators, or a combination thereof. We propose distributed control laws for the different types of manipulators to achieve and maintain the desired formation shape of the end-effectors. It is achieved by assigning virtual springs to the end-effectors for the fully-actuated ones and to the virtual end-effectors for the under-actuated ones. We study further the set of all desired and reachable shapes for the networked manipulators' end-effectors. Finally, we validate our analysis via numerical simulations.
Network motifs are recurrent, small-scale patterns of interactions observed frequently in a system. They shed light on the interplay between the topology and the dynamics of complex networks across various domains. In this work, we focus on the problem of counting occurrences of small sub-hypergraph patterns in very large hypergraphs, where higher-order interactions connect arbitrary numbers of system units. We show how directly exploiting higher-order structures speeds up the counting process compared to traditional data mining techniques for exact motif discovery. Moreover, with hyperedge sampling, performance is further improved at the cost of small errors in the estimation of motif frequency. We evaluate our method on several real-world datasets describing face-to-face interactions, co-authorship and human communication. We show that our approximated algorithm allows us to extract higher-order motifs faster and on a larger scale, beyond the computational limits of an exact approach.
We consider the task of filtering a dynamic parameter evolving as a diffusion process, given data collected at discrete times from a likelihood which is conjugate to the marginal law of the diffusion, when a generic dual process on a discrete state space is available. Recently, it was shown that duality with respect to a death-like process implies that the filtering distributions are finite mixtures, making exact filtering and smoothing feasible through recursive algorithms with polynomial complexity in the number of observations. Here we provide general results for the case of duality between the diffusion and a regular jump continuous-time Markov chain on a discrete state space, which typically leads to filtering distribution given by countable mixtures indexed by the dual process state space. We investigate the performance of several approximation strategies on two hidden Markov models driven by Cox-Ingersoll-Ross and Wright-Fisher diffusions, which admit duals of birth-and-death type, and compare them with the available exact strategies based on death-type duals and with bootstrap particle filtering on the diffusion state space as a general benchmark.
We introduce a flexible method to simultaneously infer both the drift and volatility functions of a discretely observed scalar diffusion. We introduce spline bases to represent these functions and develop a Markov chain Monte Carlo algorithm to infer, a posteriori, the coefficients of these functions in the spline basis. A key innovation is that we use spline bases to model transformed versions of the drift and volatility functions rather than the functions themselves. The output of the algorithm is a posterior sample of plausible drift and volatility functions that are not constrained to any particular parametric family. The flexibility of this approach provides practitioners a powerful investigative tool, allowing them to posit a variety of parametric models to better capture the underlying dynamics of their processes of interest. We illustrate the versatility of our method by applying it to challenging datasets from finance, paleoclimatology, and astrophysics. In view of the parametric diffusion models widely employed in the literature for those examples, some of our results are surprising since they call into question some aspects of these models.
Hopfield networks are widely used in neuroscience as simplified theoretical models of biological associative memory. The original Hopfield networks store memories by encoding patterns of binary associations, which result in a synaptic learning mechanism known as Hebbian learning rule. Modern Hopfield networks can achieve exponential capacity scaling by using highly non-linear energy functions. However, the energy function of these newer models cannot be straightforwardly compressed into binary synaptic couplings and it does not directly provide new synaptic learning rules. In this work we show that generative diffusion models can be interpreted as energy-based models and that, when trained on discrete patterns, their energy function is equivalent to that of modern Hopfield networks. This equivalence allows us to interpret the supervised training of diffusion models as a synaptic learning process that encodes the associative dynamics of a modern Hopfield network in the weight structure of a deep neural network. Accordingly, in our experiments we show that the storage capacity of a continuous modern Hopfield network is identical to the capacity of a diffusion model. Our results establish a strong link between generative modeling and the theoretical neuroscience of memory, which provide a powerful computational foundation for the reconstructive theory of memory, where creative generation and memory recall can be seen as parts of a unified continuum.
Bayesian_pyhf is a Python package that allows for the parallel Bayesian and frequentist evaluation of multi-channel binned statistical models. The Python library pyhf is used to build such models according to the HistFactory framework and already includes many frequentist inference methodologies. The pyhf-built models are then used as data-generating model for Bayesian inference and evaluated with the Python library PyMC. Based on Monte Carlo Chain Methods, PyMC allows for Bayesian modelling and together with the arviz library offers a wide range of Bayesian analysis tools.
We propose Feature-aligned N-BEATS as a domain-generalized time series forecasting model. It is a nontrivial extension of N-BEATS with doubly residual stacking principle (Oreshkin et al.[42]) into a representation learning framework. In particular, it revolves around marginal feature probability measures induced by the intricate composition of residual and feature extracting operators of N-BEATS in each stack and aligns them stack-wisely via an approximate of an optimal transport distance referred to as the Sinkhorn divergence. The training loss consists of an empirical risk minimization from multiple source domains, i.e., forecasting loss, and an alignment loss calculated with the Sinkhorn divergence, which allows the model to learn invariant features stack-wisely across multiple source data sequences while retaining N-BEATS's interpretable design and forecasting power. Comprehensive experimental evaluations with ablation studies are provided and the corresponding results demonstrate the proposed model's forecasting and generalization capabilities.
In large-scale systems there are fundamental challenges when centralised techniques are used for task allocation. The number of interactions is limited by resource constraints such as on computation, storage, and network communication. We can increase scalability by implementing the system as a distributed task-allocation system, sharing tasks across many agents. However, this also increases the resource cost of communications and synchronisation, and is difficult to scale. In this paper we present four algorithms to solve these problems. The combination of these algorithms enable each agent to improve their task allocation strategy through reinforcement learning, while changing how much they explore the system in response to how optimal they believe their current strategy is, given their past experience. We focus on distributed agent systems where the agents' behaviours are constrained by resource usage limits, limiting agents to local rather than system-wide knowledge. We evaluate these algorithms in a simulated environment where agents are given a task composed of multiple subtasks that must be allocated to other agents with differing capabilities, to then carry out those tasks. We also simulate real-life system effects such as networking instability. Our solution is shown to solve the task allocation problem to 6.7% of the theoretical optimal within the system configurations considered. It provides 5x better performance recovery over no-knowledge retention approaches when system connectivity is impacted, and is tested against systems up to 100 agents with less than a 9% impact on the algorithms' performance.
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