The success of Bayesian inference with MCMC depends critically on Markov chains rapidly reaching the posterior distribution. Despite the plentitude of inferential theory for posteriors in Bayesian non-parametrics, convergence properties of MCMC algorithms that simulate from such ideal inferential targets are not thoroughly understood. This work focuses on the Bayesian CART algorithm which forms a building block of Bayesian Additive Regression Trees (BART). We derive upper bounds on mixing times for typical posteriors under various proposal distributions. Exploiting the wavelet representation of trees, we provide sufficient conditions for Bayesian CART to mix well (polynomially) under certain hierarchical connectivity restrictions on the signal. We also derive a negative result showing that Bayesian CART (based on simple grow and prune steps) cannot reach deep isolated signals in faster than exponential mixing time. To remediate myopic tree exploration, we propose Twiggy Bayesian CART which attaches/detaches entire twigs (not just single nodes) in the proposal distribution. We show polynomial mixing of Twiggy Bayesian CART without assuming that the signal is connected on a tree. Going further, we show that informed variants achieve even faster mixing. A thorough simulation study highlights discrepancies between spike-and-slab priors and Bayesian CART under a variety of proposals.
Hawkes processes are a popular framework to model the occurrence of sequential events, i.e., occurrence dynamics, in several fields such as social diffusion. In real-world scenarios, the inter-arrival time among events is irregular. However, existing neural network-based Hawkes process models not only i) fail to capture such complicated irregular dynamics, but also ii) resort to heuristics to calculate the log-likelihood of events since they are mostly based on neural networks designed for regular discrete inputs. To this end, we present the concept of Hawkes process based on controlled differential equations (HP-CDE), by adopting the neural controlled differential equation (neural CDE) technology which is an analogue to continuous RNNs. Since HP-CDE continuously reads data, i) irregular time-series datasets can be properly treated preserving their uneven temporal spaces, and ii) the log-likelihood can be exactly computed. Moreover, as both Hawkes processes and neural CDEs are first developed to model complicated human behavioral dynamics, neural CDE-based Hawkes processes are successful in modeling such occurrence dynamics. In our experiments with 4 real-world datasets, our method outperforms existing methods by non-trivial margins.
This work introduces the first small-loss and gradual-variation regret bounds for online portfolio selection, marking the first instances of data-dependent bounds for online convex optimization with non-Lipschitz, non-smooth losses. The algorithms we propose exhibit sublinear regret rates in the worst cases and achieve logarithmic regrets when the data is "easy," with per-iteration time almost linear in the number of investment alternatives. The regret bounds are derived using novel smoothness characterizations of the logarithmic loss, a local norm-based analysis of following the regularized leader (FTRL) with self-concordant regularizers, which are not necessarily barriers, and an implicit variant of optimistic FTRL with the log-barrier.
Spacecraft and drones aimed at exploring our solar system are designed to operate in conditions where the smart use of onboard resources is vital to the success or failure of the mission. Sensorimotor actions are thus often derived from high-level, quantifiable, optimality principles assigned to each task, utilizing consolidated tools in optimal control theory. The planned actions are derived on the ground and transferred onboard where controllers have the task of tracking the uploaded guidance profile. Here we argue that end-to-end neural guidance and control architectures (here called G&CNets) allow transferring onboard the burden of acting upon these optimality principles. In this way, the sensor information is transformed in real time into optimal plans thus increasing the mission autonomy and robustness. We discuss the main results obtained in training such neural architectures in simulation for interplanetary transfers, landings and close proximity operations, highlighting the successful learning of optimality principles by the neural model. We then suggest drone racing as an ideal gym environment to test these architectures on real robotic platforms, thus increasing confidence in their utilization on future space exploration missions. Drone racing shares with spacecraft missions both limited onboard computational capabilities and similar control structures induced from the optimality principle sought, but it also entails different levels of uncertainties and unmodelled effects. Furthermore, the success of G&CNets on extremely resource-restricted drones illustrates their potential to bring real-time optimal control within reach of a wider variety of robotic systems, both in space and on Earth.
In machine learning (ML), Python serves as a convenient abstraction for working with key libraries such as PyTorch, scikit-learn, and others. Unlike DBMS, however, Python applications may lose important data, such as trained models and extracted features, due to machine failures or human errors, leading to a waste of time and resources. Specifically, they lack four essential properties that could make ML more reliable and user-friendly -- durability, atomicity, replicability, and time-versioning (DART). This paper presents our vision of Transactional Python that provides DART without any code modifications to user programs or the Python kernel, by non-intrusively monitoring application states at the object level and determining a minimal amount of information sufficient to reconstruct a whole application. Our evaluation of a proof-of-concept implementation with public PyTorch and scikit-learn applications shows that DART can be offered with overheads ranging 1.5%--15.6%.
Effective close-proximity human-robot interaction (CP-HRI) requires robots to be able to both efficiently perform tasks as well as adapt to human behavior and preferences. However, this ability is mediated by many, sometimes competing, aspects of interaction. We propose a real-time motion-planning framework for robotic manipulators that can simultaneously optimize a set of both task- and human-centric cost functions. To this end, we formulate a Nonlinear Model-Predictive Control (NMPC) problem with kino-dynamic constraints and efficiently solve it by leveraging recent advances in nonlinear trajectory optimization. We employ stochastic predictions of the human partner's trajectories in order to adapt the robot's nominal behavior in anticipation of its human partner. Our framework explicitly models and allows balancing of different task- and human-centric cost functions. While previous approaches to trajectory optimization for CP-HRI take anywhere from several seconds to a full minute to compute a trajectory, our approach is capable of computing one in 318 ms on average, enabling real-time implementation. We illustrate the effectiveness of our framework by simultaneously optimizing for separation distance, end-effector visibility, legibility, smoothness, and deviation from nominal behavior. We also demonstrate that our approach performs comparably to prior work in terms of the chosen cost functions, while significantly improving computational efficiency.
Magnesium alloys are attractive options for temporary bio-implants because of their biocompatibility, controlled corrosion rate, and similarity to natural bone in terms of stiffness and density. Nevertheless, their low mechanical strength hinders their use as cardiovascular stents and bone substitutes. While it is possible to engineer alloys with the desired mechanical strength, optimizing the mechanical properties of biocompatible magnesium alloys using conventional experimental methods is time-consuming and expensive. Therefore, Artificial Intelligence (AI) can be leveraged to streamline the alloy design process and reduce the required time. In this study, a machine learning model was developed to predict the yield strength (YS) of biocompatible magnesium alloys with an $R^2$ accuracy of 91\%. The predictive model was then validated using the CALPHAD technique and thermodynamics calculations. Next, the predictive model was employed as the fitness function of a genetic algorithm to optimize the alloy composition for high-strength biocompatible magnesium implants. As a result, two alloys were proposed and synthesized, exhibiting YS values of 108 and 113 MPa, respectively. These values were substantially higher than those of conventional magnesium biocompatible alloys and closer to the YS and compressive strength of natural bone. Finally, the synthesized alloys were subjected to microstructure analysis and mechanical property testing to validate and evaluate the performance of the proposed AI-based alloy design approach for creating alloys with specific properties suitable for diverse applications.
In this work, we introduce S4M, a new efficient speech separation framework based on neural state-space models (SSM). Motivated by linear time-invariant systems for sequence modeling, our SSM-based approach can efficiently model input signals into a format of linear ordinary differential equations (ODEs) for representation learning. To extend the SSM technique into speech separation tasks, we first decompose the input mixture into multi-scale representations with different resolutions. This mechanism enables S4M to learn globally coherent separation and reconstruction. The experimental results show that S4M performs comparably to other separation backbones in terms of SI-SDRi, while having a much lower model complexity with significantly fewer trainable parameters. In addition, our S4M-tiny model (1.8M parameters) even surpasses attention-based Sepformer (26.0M parameters) in noisy conditions with only 9.2 of multiply-accumulate operation (MACs).
Flexible laryngoscopy is commonly performed by otolaryngologists to detect laryngeal diseases and to recognize potentially malignant lesions. Recently, researchers have introduced machine learning techniques to facilitate automated diagnosis using laryngeal images and achieved promising results. Diagnostic performance can be improved when patients' demographic information is incorporated into models. However, manual entry of patient data is time consuming for clinicians. In this study, we made the first endeavor to employ deep learning models to predict patient demographic information to improve detector model performance. The overall accuracy for gender, smoking history, and age was 85.5%, 65.2%, and 75.9%, respectively. We also created a new laryngoscopic image set for machine learning study and benchmarked the performance of 8 classical deep learning models based on CNNs and Transformers. The results can be integrated into current learning models to improve their performance by incorporating the patient's demographic information.
Simulating turbulence is critical for many societally important applications in aerospace engineering, environmental science, the energy industry, and biomedicine. Large eddy simulation (LES) has been widely used as an alternative to direct numerical simulation (DNS) for simulating turbulent flows due to its reduced computational cost. However, LES is unable to capture all of the scales of turbulent transport accurately. Reconstructing DNS from low-resolution LES is critical for many scientific and engineering disciplines, but it poses many challenges to existing super-resolution methods due to the spatio-temporal complexity of turbulent flows. In this work, we propose a new physics-guided neural network for reconstructing the sequential DNS from low-resolution LES data. The proposed method leverages the partial differential equation that underlies the flow dynamics in the design of spatio-temporal model architecture. A degradation-based refinement method is also developed to enforce physical constraints and further reduce the accumulated reconstruction errors over long periods. The results on two different types of turbulent flow data confirm the superiority of the proposed method in reconstructing the high-resolution DNS data and preserving the physical characteristics of flow transport.