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Exploring the semantic context in scene images is essential for indoor scene recognition. However, due to the diverse intra-class spatial layouts and the coexisting inter-class objects, modeling contextual relationships to adapt various image characteristics is a great challenge. Existing contextual modeling methods for scene recognition exhibit two limitations: 1) They typically model only one kind of spatial relationship among objects within scenes in an artificially predefined manner, with limited exploration of diverse spatial layouts. 2) They often overlook the differences in coexisting objects across different scenes, suppressing scene recognition performance. To overcome these limitations, we propose SpaCoNet, which simultaneously models Spatial relation and Co-occurrence of objects guided by semantic segmentation. Firstly, the Semantic Spatial Relation Module (SSRM) is constructed to model scene spatial features. With the help of semantic segmentation, this module decouples the spatial information from the scene image and thoroughly explores all spatial relationships among objects in an end-to-end manner. Secondly, both spatial features from the SSRM and deep features from the Image Feature Extraction Module are allocated to each object, so as to distinguish the coexisting object across different scenes. Finally, utilizing the discriminative features above, we design a Global-Local Dependency Module to explore the long-range co-occurrence among objects, and further generate a semantic-guided feature representation for indoor scene recognition. Experimental results on three widely used scene datasets demonstrate the effectiveness and generality of the proposed method.

Recently, it has become common for applied works to combine commonly used survival analysis modeling methods, such as the multivariable Cox model and propensity score weighting, with the intention of forming a doubly robust estimator of an exposure effect hazard ratio that is unbiased in large samples when either the Cox model or the propensity score model is correctly specified. This combination does not, in general, produce a doubly robust estimator, even after regression standardization, when there is truly a causal effect. We demonstrate via simulation this lack of double robustness for the semiparametric Cox model, the Weibull proportional hazards model, and a simple proportional hazards flexible parametric model, with both the latter models fit via maximum likelihood. We provide a novel proof that the combination of propensity score weighting and a proportional hazards survival model, fit either via full or partial likelihood, is consistent under the null of no causal effect of the exposure on the outcome under particular censoring mechanisms if either the propensity score or the outcome model is correctly specified and contains all confounders. Given our results suggesting that double robustness only exists under the null, we outline two simple alternative estimators that are doubly robust for the survival difference at a given time point (in the above sense), provided the censoring mechanism can be correctly modeled, and one doubly robust method of estimation for the full survival curve. We provide R code to use these estimators for estimation and inference in the supporting information.

Linear structural vector autoregressive models can be identified statistically without imposing restrictions on the model if the shocks are mutually independent and at most one of them is Gaussian. We show that this result extends to structural threshold and smooth transition vector autoregressive models incorporating a time-varying impact matrix defined as a weighted sum of the impact matrices of the regimes. Our empirical application studies the effects of the climate policy uncertainty shock on the U.S. macroeconomy. In a structural logistic smooth transition vector autoregressive model consisting of two regimes, we find that a positive climate policy uncertainty shock decreases production in times of low economic policy uncertainty but slightly increases it in times of high economic policy uncertainty. The introduced methods are implemented to the accompanying R package sstvars.

We propose a comprehensive framework for policy gradient methods tailored to continuous time reinforcement learning. This is based on the connection between stochastic control problems and randomised problems, enabling applications across various classes of Markovian continuous time control problems, beyond diffusion models, including e.g. regular, impulse and optimal stopping/switching problems. By utilizing change of measure in the control randomisation technique, we derive a new policy gradient representation for these randomised problems, featuring parametrised intensity policies. We further develop actor-critic algorithms specifically designed to address general Markovian stochastic control issues. Our framework is demonstrated through its application to optimal switching problems, with two numerical case studies in the energy sector focusing on real options.

We present a novel solution procedure for initial boundary value problems. The procedure is based on an action principle, in which coordinate maps are included as dynamical degrees of freedom. This reparametrization invariant action is formulated in an abstract parameter space and an energy density scale associated with the space-time coordinates separates the dynamics of the coordinate maps and of the propagating fields. Treating coordinates as dependent, i.e. dynamical quantities, offers the opportunity to discretize the action while retaining all space-time symmetries and also provides the basis for automatic adaptive mesh refinement (AMR). The presence of unbroken space-time symmetries after discretization also ensures that the associated continuum Noether charges remain exactly conserved. The presence of coordinate maps in addition provides new freedom in the choice of boundary conditions. An explicit numerical example for wave propagation in $1+1$ dimensions is provided, using recently developed regularized summation-by-parts finite difference operators.

Bayesian sampling is an important task in statistics and machine learning. Over the past decade, many ensemble-type sampling methods have been proposed. In contrast to the classical Markov chain Monte Carlo methods, these new methods deploy a large number of interactive samples, and the communication between these samples is crucial in speeding up the convergence. To justify the validity of these sampling strategies, the concept of interacting particles naturally calls for the mean-field theory. The theory establishes a correspondence between particle interactions encoded in a set of coupled ODEs/SDEs and a PDE that characterizes the evolution of the underlying distribution. This bridges numerical algorithms with the PDE theory used to show convergence in time. Many mathematical machineries are developed to provide the mean-field analysis, and we showcase two such examples: The coupling method and the compactness argument built upon the martingale strategy. The former has been deployed to show the convergence of ensemble Kalman sampler and ensemble Kalman inversion, and the latter will be shown to be immensely powerful in proving the validity of the Vlasov-Boltzmann simulator.

We provide rigorous theoretical bounds for Anderson acceleration (AA) that allow for approximate calculations when applied to solve linear problems. We show that, when the approximate calculations satisfy the provided error bounds, the convergence of AA is maintained while the computational time could be reduced. We also provide computable heuristic quantities, guided by the theoretical error bounds, which can be used to automate the tuning of accuracy while performing approximate calculations. For linear problems, the use of heuristics to monitor the error introduced by approximate calculations, combined with the check on monotonicity of the residual, ensures the convergence of the numerical scheme within a prescribed residual tolerance. Motivated by the theoretical studies, we propose a reduced variant of AA, which consists in projecting the least-squares used to compute the Anderson mixing onto a subspace of reduced dimension. The dimensionality of this subspace adapts dynamically at each iteration as prescribed by the computable heuristic quantities. We numerically show and assess the performance of AA with approximate calculations on: (i) linear deterministic fixed-point iterations arising from the Richardson's scheme to solve linear systems with open-source benchmark matrices with various preconditioners and (ii) non-linear deterministic fixed-point iterations arising from non-linear time-dependent Boltzmann equations.

We study the data-driven selection of causal graphical models using constraint-based algorithms, which determine the existence or non-existence of edges (causal connections) in a graph based on testing a series of conditional independence hypotheses. In settings where the ultimate scientific goal is to use the selected graph to inform estimation of some causal effect of interest (e.g., by selecting a valid and sufficient set of adjustment variables), we argue that a "cautious" approach to graph selection should control the probability of falsely removing edges and prefer dense, rather than sparse, graphs. We propose a simple inversion of the usual conditional independence testing procedure: to remove an edge, test the null hypothesis of conditional association greater than some user-specified threshold, rather than the null of independence. This equivalence testing formulation to testing independence constraints leads to a procedure with desriable statistical properties and behaviors that better match the inferential goals of certain scientific studies, for example observational epidemiological studies that aim to estimate causal effects in the face of causal model uncertainty. We illustrate our approach on a data example from environmental epidemiology.

We propose a quantum soft-covering problem for a given general quantum channel and one of its output states, which consists in finding the minimum rank of an input state needed to approximate the given channel output. We then prove a one-shot quantum covering lemma in terms of smooth min-entropies by leveraging decoupling techniques from quantum Shannon theory. This covering result is shown to be equivalent to a coding theorem for rate distortion under a posterior (reverse) channel distortion criterion by two of the present authors. Both one-shot results directly yield corollaries about the i.i.d. asymptotics, in terms of the coherent information of the channel. The power of our quantum covering lemma is demonstrated by two additional applications: first, we formulate a quantum channel resolvability problem, and provide one-shot as well as asymptotic upper and lower bounds. Secondly, we provide new upper bounds on the unrestricted and simultaneous identification capacities of quantum channels, in particular separating for the first time the simultaneous identification capacity from the unrestricted one, proving a long-standing conjecture of the last author.

Topology optimization is an important basis for the design of components. Here, the optimal structure is found within a design space subject to boundary conditions. Thereby, the specific material law has a strong impact on the final design. An important kind of material behavior is hardening: then a, for instance, linear-elastic structure is not optimal if plastic deformation will be induced by the loads. Since hardening behavior has a remarkable impact on the resultant stress field, it needs to be accounted for during topology optimization. In this contribution, we present an extension of the thermodynamic topology optimization that accounts for this non-linear material behavior due to the evolution of plastic strains. For this purpose, we develop a novel surrogate model that allows to compute the plastic strain tensor corresponding to the current structure design for arbitrary hardening behavior. We show the agreement of the model with the classic plasticity model for monotonic loading. Furthermore, we demonstrate the interaction of the topology optimization for hardening material behavior results in structural changes.