In the teacher-student scenario under the assumption that the teacher's couplings are sparse and the student does not know the graphical structure, the learning curve and order parameters are assessed in the typical case using the replica and cavity methods from statistical mechanics. Our formulation is also applicable to a certain class of cost functions having locality; the standard likelihood does not belong to that class. The derived analytical formulas indicate that the perfect inference of the presence/absence of the teacher's couplings is possible in the thermodynamic limit taking the number of spins N as infinity while keeping the dataset size M proportional to N, as long as α M/N 2. Meanwhile, the formulas also show that the estimated coupling values corresponding to the truly existing ones in the teacher tend to be overestimated in the absolute value, manifesting the presence of estimation bias. These results are considered to be exact in the thermodynamic limit on locally treelike networks, such as the regular random or Erd os-R enyi graphs. Numerical simulation results fully support the theoretical predictions. Additional biases in the estimators on loopy graphs are also discussed. 1 Introduction Inference based on the classical Ising model is called the inverse Ising problem or Boltzmann machine learning, which is attracting more and more attention with the increasing interest in machine learning technologies.

We propose a general method for constructing hypothesis tests and confidence sets that have finite sample guarantees without regularity conditions. We refer to such procedures as ``universal.'' The method is very simple and is based on a modified version of the usual likelihood ratio statistic, that we call ``the split likelihood ratio test'' (split LRT). The method is especially appealing for irregular statistical models. Canonical examples include mixture models and models that arise in shape-constrained inference. %mixture models and shape-constrained models are just two examples. Constructing tests and confidence sets for such models is notoriously difficult. Typical inference methods, like the likelihood ratio test, are not useful in these cases because they have intractable limiting distributions. In contrast, the method we suggest works for any parametric model and also for some nonparametric models. The split LRT can also be used with profile likelihoods to deal with nuisance parameters, and it can also be run sequentially to yield anytime-valid $p$-values and confidence sequences.

Crowdsourcing is a relatively economic and efficient solution to collect annotations from the crowd through online platforms. Answers collected from workers with different expertise may be noisy and unreliable, and the quality of annotated data needs to be further maintained. Various solutions have been attempted to obtain high-quality annotations. However, they all assume that workers' label quality is stable over time (always at the same level whenever they conduct the tasks). In practice, workers' attention level changes over time, and the ignorance of which can affect the reliability of the annotations. In this paper, we focus on a novel and realistic crowdsourcing scenario involving attention-aware annotations. We propose a new probabilistic model that takes into account workers' attention to estimate the label quality. Expectation propagation is adopted for efficient Bayesian inference of our model, and a generalized Expectation Maximization algorithm is derived to estimate both the ground truth of all tasks and the label-quality of each individual crowd worker with attention. In addition, the number of tasks best suited for a worker is estimated according to changes in attention. Experiments against related methods on three real-world and one semi-simulated datasets demonstrate that our method quantifies the relationship between workers' attention and label-quality on the given tasks, and improves the aggregated labels.

We start with the distinction of outcome- and belief-based Bayesian models of the sequential update of agents' beliefs and subjective reliability of sources (trust). We then focus on discussing the influential Bayesian model of belief-based trust update by Eric Olsson, which models dichotomic events and explicitly represents anti-reliability. After sketching some disastrous recent results for this perhaps most promising model of belief update, we show new simulation results for the temporal dynamics of learning belief with and without trust update and with and without communication. The results seem to shed at least a somewhat more positive light on the communicating-and-trust-updating agents. This may be a light at the end of the tunnel of belief-based models of trust updating, but the interpretation of the clear findings is much less clear.

NumPyro is a lightweight library that provides an alternate NumPy backend to the Pyro probabilistic programming language with the same modeling interface, language primitives and effect handling abstractions. Effect handlers allow Pyro's modeling API to be extended to NumPyro despite its being built atop a fundamentally different JAX-based functional backend. In this work, we demonstrate the power of composing Pyro's effect handlers with the program transformations that enable hardware acceleration, automatic differentiation, and vectorization in JAX. In particular, NumPyro provides an iterative formulation of the No-U-Turn Sampler (NUTS) that can be end-to-end JIT compiled, yielding an implementation that is much faster than existing alternatives in both the small and large dataset regimes.

These challenges can be addressed by enforcing sparsity in the series representation through retaining only the most important basis terms. In this work, we present a novel sparse Bayesian learning technique for obtaining sparse Polynomial Chaos expansions which is based on a Relevance Vector Machine model and is trained using Variational Inference. The methodology shows great potential in high-dimensional data-driven settings using relatively few data points and achieves user-controlled sparse levels that are comparable to other methods such as compressive sensing. The proposed approach is illustrated on two numerical examples, a synthetic response function that is explored for validation purposes and a low-carbon steel plate with random Young's modulus and random loading, which is modelled by stochastic finite element with 38 input random variables.

The Hamlyn Centre for Robotic Surgery, Imperial College London, UK 2. Institute of Medical Robotics, Shanghai Jiao Tong University, ChinaAbstract Artificial Intelligence (AI) is gradually changing the practice of surgery with the advanced technological development of imaging, navigation and robotic intervention. In this article, the recent successful and influential applications of AI in surgery are reviewed from preoperative planning and intra-operative guidance to the integration of surgical robots. We end with summarizing the current state, emerging trends and major challenges in the future development of AI in surgery. Keywords: Artificial intelligence, Surgical autonomy, Medical robotics, Deep learning 1. Introduction Advances in surgery have made a significant impact on the management of both acute and chronic diseases, prolonging life and continuously extending the boundary of survival. These advances are underpinned by continuing technological developments in diagnosis, imaging, and surgical instrumentation. Complex surgical navigation and planning are made possible through the use of both pre-and intra-operative imaging techniques such as ultrasound, Computed Tomography (CT), and Magnetic Resonance Imaging Preprint submitted to Frontiers of Medicine January 6, 2020 arXiv:2001.00627v1 Many terminal illnesses have been transformed into clinically manageable chronic lifelong conditions and increasing surgery is focused on the systematic level impact on patients, avoiding isolated surgical treatment or anatomical alteration, with careful consideration of metabolic, haemodynamic and neurohormonal consequences that can influence the quality of life. For recent advances in medicine, AI has played an important role in clinical decision support since the early years of developing the MYCIN system [5]. AI is now increasingly used for risk stratification, genomics, imaging and diagnosis, precision medicine, and drug discovery. The introduction of AI in surgery is more recent and it has a strong root in imaging and navigation, with early techniques focused on feature detection and computer assisted intervention for both preoperative planning and intra-operative guidance. Over the years, supervised algorithms such as active shape models, atlas based methods and statistical classifiers have been developed [1]. With recent successes of AlexNet [6], deep learning methods, especially Deep Con-volutional Neural Network (DCNN) where multiple convolutional layers are cascaded, have enabled automatically learned data-driven descriptors, rather than ad hoc handcrafted features, to be used for image understanding with improved robustness and generalizability.

Data ownership and data protection are increasingly important topics with ethical and legal implications, e.g., with the right to erasure established in the European General Data Protection Regulation (GDPR). In this light, we investigate network embeddings, i.e., the representation of network nodes as low-dimensional vectors. We consider a typical social network scenario with nodes representing users and edges relationships between them. We assume that a network embedding of the nodes has been trained. After that, a user demands the removal of his data, requiring the full deletion of the corresponding network information, in particular the corresponding node and incident edges. In that setting, we analyze whether after the removal of the node from the network and the deletion of the vector representation of the respective node in the embedding significant information about the link structure of the removed node is still encoded in the embedding vectors of the remaining nodes. This would require a (potentially computationally expensive) retraining of the embedding. For that purpose, we deploy an attack that leverages information from the remaining network and embedding to recover information about the neighbors of the removed node. The attack is based on (i) measuring distance changes in network embeddings and (ii) a machine learning classifier that is trained on networks that are constructed by removing additional nodes. Our experiments demonstrate that substantial information about the edges of a removed node/user can be retrieved across many different datasets. This implies that to fully protect the privacy of users, node deletion requires complete retraining - or at least a significant modification - of original network embeddings. Our results suggest that deleting the corresponding vector representation from network embeddings alone is not sufficient from a privacy perspective.

In this work, we develop Gaussian process regression (GPR) models of hyperelastic material behavior. First, we consider the direct approach of modeling the components of the Cauchy stress tensor as a function of the components of the Finger stretch tensor in a Gaussian process. We then consider an improvement on this approach that embeds rotational invariance of the stress-stretch constitutive relation in the GPR representation. This approach requires fewer training examples and achieves higher accuracy while maintaining invariance to rotations exactly. Finally, we consider an approach that recovers the strain-energy density function and derives the stress tensor from this potential. Although the error of this model for predicting the stress tensor is higher, the strain-energy density is recovered with high accuracy from limited training data. The approaches presented here are examples of physics-informed machine learning. They go beyond purely data-driven approaches by embedding the physical system constraints directly into the Gaussian process representation of materials models.

We introduce a procedure for predictive conditional density estimation under logarithmic loss, which we call SMP (Sample Minmax Predictor). This predictor minimizes a new general excess risk bound, which critically remains valid under model misspecification. On standard examples, this bound scales as $d/n$ where $d$ is the dimension of the model and $n$ the sample size, regardless of the true distribution. The SMP, which is an improper (out-of-model) procedure, improves over proper (within-model) estimators (such as the maximum likelihood estimator), whose excess risk can degrade arbitrarily in the misspecified case. For density estimation, our bounds improve over approaches based on online-to-batch conversion, by removing suboptimal $\log n$ factors, addressing an open problem from Gr{\"u}nwald and Kot{\l}owski (2011) for the considered models. For the Gaussian linear model, the SMP admits an explicit expression, and its expected excess risk in the general misspecified case is at most twice the minimax excess risk in the \emph{well-specified case}, but without any condition on the noise variance or approximation error of the linear model. For logistic regression, a penalized SMP can be computed efficiently by training two logistic regressions, and achieves a non-asymptotic excess risk of $O((d + B^2R^2)/n)$, where $R$ is a bound on the norm of the features and $B$ the norm of the comparison linear predictor. This improves the rates of proper (within-model) estimators, since such procedures can achieve no better rate than $\min(BR/\sqrt{n},de^{BR}/n)$ in general. This also provides a computationally more efficient alternative to approaches based on online-to-batch conversion of Bayesian mixture procedures, which require approximate posterior sampling, thereby partly answering a question by Foster et al. (2018).