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Resource constrained project scheduling is an important combinatorial optimisation problem with many practical applications. With complex requirements such as precedence constraints, limited resources, and finance-based objectives, finding optimal solutions for large problem instances is very challenging even with well-customised meta-heuristics and matheuristics. To address this challenge, we propose a new math-heuristic algorithm based on Merge Search and parallel computing to solve the resource constrained project scheduling with the aim of maximising the net present value. This paper presents a novel matheuristic framework designed for resource constrained project scheduling, Merge search, which is a variable partitioning and merging mechanism to formulate restricted mixed integer programs with the aim of improving an existing pool of solutions. The solution pool is obtained via a customised parallel ant colony optimisation algorithm, which is also capable of generating high quality solutions on its own. The experimental results show that the proposed method outperforms the current state-of-the-art algorithms on known benchmark problem instances. Further analyses also demonstrate that the proposed algorithm is substantially more efficient compared to its counterparts in respect to its convergence properties when considering multiple cores.

Real-time scheduling theory assists developers of embedded systems in verifying that the timing constraints required by critical software tasks can be feasibly met on a given hardware platform. Fundamental problems in the theory are often formulated as search problems for fixed points of functions and are solved by fixed-point iterations. These fixed-point methods are used widely because they are simple to understand, simple to implement, and seem to work well in practice. These fundamental problems can also be formulated as integer programs and solved with algorithms that are based on theories of linear programming and cutting planes amongst others. However, such algorithms are harder to understand and implement than fixed-point iterations. In this research, we show that ideas like linear programming duality and cutting planes can be used to develop algorithms that are as easy to implement as existing fixed-point iteration schemes but have better convergence properties. We evaluate the algorithms on synthetically generated problem instances to demonstrate that the new algorithms are faster than the existing algorithms.

Concerns about the reproducibility of deep learning research are more prominent than ever, with no clear solution in sight. The relevance of machine learning research can only be improved if we also employ empirical rigor that incorporates reproducibility guidelines, especially so in the medical imaging field. The Medical Imaging with Deep Learning (MIDL) conference has made advancements in this direction by advocating open access, and recently also recommending authors to make their code public - both aspects being adopted by the majority of the conference submissions. This helps the reproducibility of the methods, however, there is currently little or no support for further evaluation of these supplementary material, making them vulnerable to poor quality, which affects the impact of the entire submission. We have evaluated all accepted full paper submissions to MIDL between 2018 and 2022 using established, but slightly adjusted guidelines on reproducibility and the quality of the public repositories. The evaluations show that publishing repositories and using public datasets are becoming more popular, which helps traceability, but the quality of the repositories has not improved over the years, leaving room for improvement in every aspect of designing repositories. Merely 22% of all submissions contain a repository that were deemed repeatable using our evaluations. From the commonly encountered issues during the evaluations, we propose a set of guidelines for machine learning-related research for medical imaging applications, adjusted specifically for future submissions to MIDL.

This article describes a method to estimate the mortality rate ratio R from current status data with duration in a chronic condition in case the general mortality of the overall population is known. Apart from the general mortality, the method requires four pieces of information from the study participants: age and time at the survey/interview, whether the chronic condition is present (current status) and if so, for how long the condition is present (duration). The method uses a differential equation that relates prevalence, incidence and mortality to estimate R of the people with the chronic condition compared to those without the condition. To demonstrate feasibility, a simulation based on the illness-death model (multi-state model) with transition rates motivated from long-term care is run. It is found that the method requires a large number of study participants (100000 or more) to estimate R with a reasonably low relative error. Despite the large sample size, the method can be useful in settings when cross-sectional information are easily available, e.g., in claims data, and national age-specific general mortality rates are accessible from vital statistics.

In statistical inference, uncertainty is unknown and all models are wrong. That is to say, a person who makes a statistical model and a prior distribution is simultaneously aware that both are fictional candidates. To study such cases, statistical measures have been constructed, such as cross validation, information criteria, and marginal likelihood, however, their mathematical properties have not yet been completely clarified when statistical models are under- and over- parametrized. We introduce a place of mathematical theory of Bayesian statistics for unknown uncertainty, which clarifies general properties of cross validation, information criteria, and marginal likelihood, even if an unknown data-generating process is unrealizable by a model or even if the posterior distribution cannot be approximated by any normal distribution. Hence it gives a helpful standpoint for a person who cannot believe in any specific model and prior. This paper consists of three parts. The first is a new result, whereas the second and third are well-known previous results with new experiments. We show there exists a more precise estimator of the generalization loss than leave-one-out cross validation, there exists a more accurate approximation of marginal likelihood than BIC, and the optimal hyperparameters for generalization loss and marginal likelihood are different.

We propose a generalization of the synthetic control and synthetic interventions methodology to the dynamic treatment regime. We consider the estimation of unit-specific treatment effects from panel data collected via a dynamic treatment regime and in the presence of unobserved confounding. That is, each unit receives multiple treatments sequentially, based on an adaptive policy, which depends on a latent endogenously time-varying confounding state of the treated unit. Under a low-rank latent factor model assumption and a technical overlap assumption we propose an identification strategy for any unit-specific mean outcome under any sequence of interventions. The latent factor model we propose admits linear time-varying and time-invariant dynamical systems as special cases. Our approach can be seen as an identification strategy for structural nested mean models under a low-rank latent factor assumption on the blip effects. Our method, which we term "synthetic blip effects", is a backwards induction process, where the blip effect of a treatment at each period and for a target unit is recursively expressed as linear combinations of blip effects of a carefully chosen group of other units that received the designated treatment. Our work avoids the combinatorial explosion in the number of units that would be required by a vanilla application of prior synthetic control and synthetic intervention methods in such dynamic treatment regime settings.

Complex prediction models such as deep learning are the output from fitting machine learning, neural networks, or AI models to a set of training data. These are now standard tools in science. A key challenge with the current generation of models is that they are highly parameterized, which makes describing and interpreting the prediction strategies difficult. We use topological data analysis to transform these complex prediction models into pictures representing a topological view. The result is a map of the predictions that enables inspection. The methods scale up to large datasets across different domains and enable us to detect labeling errors in training data, understand generalization in image classification, and inspect predictions of likely pathogenic mutations in the BRCA1 gene.

In deep reinforcement learning (RL), data augmentation is widely considered as a tool to induce a set of useful priors about semantic consistency and improve sample efficiency and generalization performance. However, even when the prior is useful for generalization, distilling it to RL agent often interferes with RL training and degenerates sample efficiency. Meanwhile, the agent is forgetful of the prior due to the non-stationary nature of RL. These observations suggest two extreme schedules of distillation: (i) over the entire training; or (ii) only at the end. Hence, we devise a stand-alone network distillation method to inject the consistency prior at any time (even after RL), and a simple yet efficient framework to automatically schedule the distillation. Specifically, the proposed framework first focuses on mastering train environments regardless of generalization by adaptively deciding which {\it or no} augmentation to be used for the training. After this, we add the distillation to extract the remaining benefits for generalization from all the augmentations, which requires no additional new samples. In our experiments, we demonstrate the utility of the proposed framework, in particular, that considers postponing the augmentation to the end of RL training.

This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the output of trained networks by solving layer-to-layer iteration equations and nonlinear learning dynamics. A main result is that the predictions of networks are described by nearly-Gaussian distributions, with the depth-to-width aspect ratio of the network controlling the deviations from the infinite-width Gaussian description. We explain how these effectively-deep networks learn nontrivial representations from training and more broadly analyze the mechanism of representation learning for nonlinear models. From a nearly-kernel-methods perspective, we find that the dependence of such models' predictions on the underlying learning algorithm can be expressed in a simple and universal way. To obtain these results, we develop the notion of representation group flow (RG flow) to characterize the propagation of signals through the network. By tuning networks to criticality, we give a practical solution to the exploding and vanishing gradient problem. We further explain how RG flow leads to near-universal behavior and lets us categorize networks built from different activation functions into universality classes. Altogether, we show that the depth-to-width ratio governs the effective model complexity of the ensemble of trained networks. By using information-theoretic techniques, we estimate the optimal aspect ratio at which we expect the network to be practically most useful and show how residual connections can be used to push this scale to arbitrary depths. With these tools, we can learn in detail about the inductive bias of architectures, hyperparameters, and optimizers.

Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use as a layer in neural networks trained by backpropagation. To address this issue, we propose to smooth the max operator in the dynamic programming recursion, using a strongly convex regularizer. This allows to relax both the optimal value and solution of the original combinatorial problem, and turns a broad class of DP algorithms into differentiable operators. Theoretically, we provide a new probabilistic perspective on backpropagating through these DP operators, and relate them to inference in graphical models. We derive two particular instantiations of our framework, a smoothed Viterbi algorithm for sequence prediction and a smoothed DTW algorithm for time-series alignment. We showcase these instantiations on two structured prediction tasks and on structured and sparse attention for neural machine translation.