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We address a classical problem in statistics: adding two-way interaction terms to a regression model. As the covariate dimension increases quadratically, we develop an estimator that adapts well to this increase, while providing accurate estimates and appropriate inference. Existing strategies overcome the dimensionality problem by only allowing interactions between relevant main effects. Building on this philosophy, we implement a softer link between the two types of effects using a local shrinkage model. We empirically show that borrowing strength between the amount of shrinkage for main effects and their interactions can strongly improve estimation of the regression coefficients. Moreover, we evaluate the potential of the model for inference, which is notoriously hard for selection strategies. Large-scale cohort data are used to provide realistic illustrations and evaluations. Comparisons with other methods are provided. The evaluation of variable importance is not trivial in regression models with many interaction terms. Therefore, we derive a new analytical formula for the Shapley value, which enables rapid assessment of individual-specific variable importance scores and their uncertainties. Finally, while not targeting for prediction, we do show that our models can be very competitive to a more advanced machine learner, like random forest, even for fairly large sample sizes. The implementation of our method in RStan is fairly straightforward, allowing for adjustments to specific needs.

Speech applications in far-field real world settings often deal with signals that are corrupted by reverberation. The task of dereverberation constitutes an important step to improve the audible quality and to reduce the error rates in applications like automatic speech recognition (ASR). We propose a unified framework of speech dereverberation for improving the speech quality and the ASR performance using the approach of envelope-carrier decomposition provided by an autoregressive (AR) model. The AR model is applied in the frequency domain of the sub-band speech signals to separate the envelope and carrier parts. A novel neural architecture based on dual path long short term memory (DPLSTM) model is proposed, which jointly enhances the sub-band envelope and carrier components. The dereverberated envelope-carrier signals are modulated and the sub-band signals are synthesized to reconstruct the audio signal back. The DPLSTM model for dereverberation of envelope and carrier components also allows the joint learning of the network weights for the down stream ASR task. In the ASR tasks on the REVERB challenge dataset as well as on the VOiCES dataset, we illustrate that the joint learning of speech dereverberation network and the E2E ASR model yields significant performance improvements over the baseline ASR system trained on log-mel spectrogram as well as other benchmarks for dereverberation (average relative improvements of 10-24% over the baseline system). The speech quality improvements, evaluated using subjective listening tests, further highlight the improved quality of the reconstructed audio.

What is the optimal way to approximate a high-dimensional diffusion process by one in which the coordinates are independent? This paper presents a construction, called the \emph{independent projection}, which is optimal for two natural criteria. First, when the original diffusion is reversible with invariant measure $\rho_*$, the independent projection serves as the Wasserstein gradient flow for the relative entropy $H(\cdot\,|\,\rho_*)$ constrained to the space of product measures. This is related to recent Langevin-based sampling schemes proposed in the statistical literature on mean field variational inference. In addition, we provide both qualitative and quantitative results on the long-time convergence of the independent projection, with quantitative results in the log-concave case derived via a new variant of the logarithmic Sobolev inequality. Second, among all processes with independent coordinates, the independent projection is shown to exhibit the slowest growth rate of path-space entropy relative to the original diffusion. This sheds new light on the classical McKean-Vlasov equation and recent variants proposed for non-exchangeable systems, which can be viewed as special cases of the independent projection.

Discovering causal relationships from observational data is a fundamental yet challenging task. In some applications, it may suffice to learn the causal features of a given response variable, instead of learning the entire underlying causal structure. Invariant causal prediction (ICP, Peters et al., 2016) is a method for causal feature selection which requires data from heterogeneous settings. ICP assumes that the mechanism for generating the response from its direct causes is the same in all settings and exploits this invariance to output a subset of the causal features. The framework of ICP has been extended to general additive noise models and to nonparametric settings using conditional independence testing. However, nonparametric conditional independence testing often suffers from low power (or poor type I error control) and the aforementioned parametric models are not suitable for applications in which the response is not measured on a continuous scale, but rather reflects categories or counts. To bridge this gap, we develop ICP in the context of transformation models (TRAMs), allowing for continuous, categorical, count-type, and uninformatively censored responses (we show that, in general, these model classes do not allow for identifiability when there is no exogenous heterogeneity). We propose TRAM-GCM, a test for invariance of a subset of covariates, based on the expected conditional covariance between environments and score residuals which satisfies uniform asymptotic level guarantees. For the special case of linear shift TRAMs, we propose an additional invariance test, TRAM-Wald, based on the Wald statistic. We implement both proposed methods in the open-source R package "tramicp" and show in simulations that under the correct model specification, our approach empirically yields higher power than nonparametric ICP based on conditional independence testing.

Most existing methods for unsupervised industrial anomaly detection train a separate model for each object category. This kind of approach can easily capture the category-specific feature distributions, but results in high storage cost and low training efficiency. In this paper, we propose a unified mixed-attention auto encoder (MAAE) to implement multi-class anomaly detection with a single model. To alleviate the performance degradation due to the diverse distribution patterns of different categories, we employ spatial attentions and channel attentions to effectively capture the global category information and model the feature distributions of multiple classes. Furthermore, to simulate the realistic noises on features and preserve the surface semantics of objects from different categories which are essential for detecting the subtle anomalies, we propose an adaptive noise generator and a multi-scale fusion module for the pre-trained features. MAAE delivers remarkable performances on the benchmark dataset compared with the state-of-the-art methods.

Surface defect inspection is of great importance for industrial manufacture and production. Though defect inspection methods based on deep learning have made significant progress, there are still some challenges for these methods, such as indistinguishable weak defects and defect-like interference in the background. To address these issues, we propose a transformer network with multi-stage CNN (Convolutional Neural Network) feature injection for surface defect segmentation, which is a UNet-like structure named CINFormer. CINFormer presents a simple yet effective feature integration mechanism that injects the multi-level CNN features of the input image into different stages of the transformer network in the encoder. This can maintain the merit of CNN capturing detailed features and that of transformer depressing noises in the background, which facilitates accurate defect detection. In addition, CINFormer presents a Top-K self-attention module to focus on tokens with more important information about the defects, so as to further reduce the impact of the redundant background. Extensive experiments conducted on the surface defect datasets DAGM 2007, Magnetic tile, and NEU show that the proposed CINFormer achieves state-of-the-art performance in defect detection.

In surgery, the application of appropriate force levels is critical for the success and safety of a given procedure. While many studies are focused on measuring in situ forces, little attention has been devoted to relating these observed forces to surgical techniques. Answering questions like "Can certain changes to a surgical technique result in lower forces and increased safety margins?" could lead to improved surgical practice, and importantly, patient outcomes. However, such studies would require a large number of trials and professional surgeons, which is generally impractical to arrange. Instead, we show how robots can learn several variations of a surgical technique from a smaller number of surgical demonstrations and interpolate learnt behaviour via a parameterised skill model. This enables a large number of trials to be performed by a robotic system and the analysis of surgical techniques and their downstream effects on tissue. Here, we introduce a parameterised model of the elliptical excision skill and apply a Bayesian optimisation scheme to optimise the excision behaviour with respect to expert ratings, as well as individual characteristics of excision forces. Results show that the proposed framework can successfully align the generated robot behaviour with subjects across varying levels of proficiency in terms of excision forces.

We consider a one-dimensional singularly perturbed 4th order problem with the additional feature of a shift term. An expansion into a smooth term, boundary layers and an inner layer yields a formal solution decomposition, and together with a stability result we have estimates for the subsequent numerical analysis. With classical layer adapted meshes we present a numerical method, that achieves supercloseness and optimal convergence orders in the associated energy norm. We also consider coarser meshes in view of the weak layers. Some numerical examples conclude the paper and support the theory.

We consider a sharp interface formulation for the multi-phase Mullins-Sekerka flow. The flow is characterized by a network of curves evolving such that the total surface energy of the curves is reduced, while the areas of the enclosed phases are conserved. Making use of a variational formulation, we introduce a fully discrete finite element method. Our discretization features a parametric approximation of the moving interfaces that is independent of the discretization used for the equations in the bulk. The scheme can be shown to be unconditionally stable and to satisfy an exact volume conservation property. Moreover, an inherent tangential velocity for the vertices on the discrete curves leads to asymptotically equidistributed vertices, meaning no remeshing is necessary in practice. Several numerical examples, including a convergence experiment for the three-phase Mullins-Sekerka flow, demonstrate the capabilities of the introduced method.

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.