Reliably and physically accurately transferring information between images through deformable image registration with large anatomical differences is an open challenge in medical image analysis. Most existing methods have two key shortcomings: first, they require extensive up-front parameter tuning to each specific registration problem, and second, they have difficulty capturing large deformations and content mismatches between images. There have however been developments that have laid the foundation for potential solutions to both shortcomings. Towards the first shortcoming, a multi-objective optimization approach using the Real-Valued Gene-pool Optimal Mixing Evolutionary Algorithm (RV-GOMEA) has been shown to be capable of producing a diverse set of registrations for 2D images in one run of the algorithm, representing different trade-offs between conflicting objectives in the registration problem. This allows the user to select a registration afterwards and removes the need for up-front tuning. Towards the second shortcoming, a dual-dynamic grid transformation model has proven effective at capturing large differences in 2D images. These two developments have recently been accelerated through GPU parallelization, delivering large speed-ups. Based on this accelerated version, it is now possible to extend the approach to 3D images. Concordantly, this work introduces the first method for multi-objective 3D deformable image registration, using a 3D dual-dynamic grid transformation model based on simplex meshes while still supporting the incorporation of annotated guidance information and multi-resolution schemes. Our proof-of-concept prototype shows promising results on synthetic and clinical 3D registration problems, forming the foundation for a new, insightful method that can include bio-mechanical properties in the registration.

Energy disaggregation, known in the literature as Non-Intrusive Load Monitoring (NILM), is the task of inferring the energy consumption of each appliance given the aggregate signal recorded by a single smart meter. In this paper, we propose a novel two-stage optimization-based approach for energy disaggregation. In the first phase, a small training set consisting of disaggregated power profiles is used to estimate the parameters and the power states by solving a mixed integer programming problem. Once the model parameters are estimated, the energy disaggregation problem is formulated as a constrained binary quadratic optimization problem. We incorporate penalty terms that exploit prior knowledge on how the disaggregated traces are generated, and appliance-specific constraints characterizing the signature of different types of appliances operating simultaneously. Our approach is compared with existing optimization-based algorithms both on a synthetic dataset and on three real-world datasets. The proposed formulation is computationally efficient, able to disambiguate loads with similar consumption patterns, and successfully reconstruct the signatures of known appliances despite the presence of unmetered devices, thus overcoming the main drawbacks of the optimization-based methods available in the literature.

We propose an extended generalization of the pseudo Huber loss formulation. We show that using the log-exp transform together with the logistic function, we can create a loss which combines the desirable properties of the strictly convex losses with robust loss functions. With this formulation, we show that a linear convergence algorithm can be utilized to find a minimizer. We further discuss the creation of a quasi-convex composite loss and provide a derivative-free exponential convergence rate algorithm.

Mathematical optimization (MO) technologies are being utilized today by leading global companies across industries – including aviation, energy, finance, logistics, telecommunications, manufacturing, media, and many more – to solve a wide range of complex, real-world problems, make optimal, data-driven decisions, and achieve greater operational efficiency. An increasing number of data scientists are adding MO into their analytics toolbox and developing applications that combine MO and machine learning (ML) technologies. In this series of webinars, we will show you how – with MO techniques – you can build interpretable models to tackle your prediction and classification problems. How to formulate an MO model. How to build an MO model using the Gurobi Python API.

From simulating new and more efficient materials to predicting how the stock market will change with greater precision, the ramifications of quantum computing for businesses are potentially huge. The world's biggest companies are now launching quantum computing programs, and governments are pouring money into quantum research. For systems that have yet prove useful, quantum computers are certainly garnering lots of attention. Quantum computers offer great promise for cryptography and optimization problems, and companies are racing to make them practical for business use. ZDNet explores what quantum computers will and won't be able to do, and the challenges that remain.

Evolutionary strategies have recently been shown to achieve competing levels of performance for complex optimization problems in reinforcement learning. In such problems, one often needs to optimize an objective function subject to a set of constraints, including for instance constraints on the entropy of a policy or to restrict the possible set of actions or states accessible to an agent. Convergence guarantees for evolutionary strategies to optimize stochastic constrained problems are however lacking in the literature. In this work, we address this problem by designing a novel optimization algorithm with a sufficient decrease mechanism that ensures convergence and that is based only on estimates of the functions. We demonstrate the applicability of this algorithm on two types of experiments: i) a control task for maximizing rewards and ii) maximizing rewards subject to a non-relaxable set of constraints.

Sequential model-based optimization sequentially selects a candidate point by constructing a surrogate model with the history of evaluations, to solve a black-box optimization problem. Gaussian process (GP) regression is a popular choice as a surrogate model, because of its capability of calculating prediction uncertainty analytically. On the other hand, an ensemble of randomized trees is another option and has practical merits over GPs due to its scalability and easiness of handling continuous/discrete mixed variables. In this paper we revisit various ensembles of randomized trees to investigate their behavior in the perspective of prediction uncertainty estimation. Then, we propose a new way of constructing an ensemble of randomized trees, referred to as BwO forest, where bagging with oversampling is employed to construct bootstrapped samples that are used to build randomized trees with random splitting. Experimental results demonstrate the validity and good performance of BwO forest over existing tree-based models in various circumstances.

The fluctuation effect of gradient expectation and variance caused by parameter update between consecutive iterations is neglected or confusing by current mainstream gradient optimization algorithms.Using this fluctuation effect, combined with the stratified sampling strategy, this paper designs a novel \underline{M}emory \underline{S}tochastic s\underline{T}ratified Gradient Descend(\underline{MST}GD) algorithm with an exponential convergence rate. Specifically, MSTGD uses two strategies for variance reduction: the first strategy is to perform variance reduction according to the proportion p of used historical gradient, which is estimated from the mean and variance of sample gradients before and after iteration, and the other strategy is stratified sampling by category. The statistic \ $\bar{G}_{mst}$\ designed under these two strategies can be adaptively unbiased, and its variance decays at a geometric rate. This enables MSTGD based on $\bar{G}_{mst}$ to obtain an exponential convergence rate of the form $\lambda^{2(k-k_0)}$($\lambda\in (0,1)$,k is the number of iteration steps,$\lambda$ is a variable related to proportion p).Unlike most other algorithms that claim to achieve an exponential convergence rate, the convergence rate is independent of parameters such as dataset size N, batch size n, etc., and can be achieved at a constant step size.Theoretical and experimental results show the effectiveness of MSTGD

The optimistic gradient method has seen increasing popularity as an efficient first-order method for solving convex-concave saddle point problems. To analyze its iteration complexity, a recent work [arXiv:1901.08511] proposed an interesting perspective that interprets the optimistic gradient method as an approximation to the proximal point method. In this paper, we follow this approach and distill the underlying idea of optimism to propose a generalized optimistic method, which encompasses the optimistic gradient method as a special case. Our general framework can handle constrained saddle point problems with composite objective functions and can work with arbitrary norms with compatible Bregman distances. Moreover, we also develop an adaptive line search scheme to select the stepsizes without knowledge of the smoothness coefficients. We instantiate our method with first-order, second-order and higher-order oracles and give sharp global iteration complexity bounds. When the objective function is convex-concave, we show that the averaged iterates of our $p$-th-order method ($p\geq 1$) converge at a rate of $\mathcal{O}(1/N^\frac{p+1}{2})$. When the objective function is further strongly-convex-strongly-concave, we prove a complexity bound of $\mathcal{O}(\frac{L_1}{\mu}\log\frac{1}{\epsilon})$ for our first-order method and a bound of $\mathcal{O}((L_p D^\frac{p-1}{2}/\mu)^{\frac{2}{p+1}}+\log\log\frac{1}{\epsilon})$ for our $p$-th-order method ($p\geq 2$) respectively, where $L_p$ ($p\geq 1$) is the Lipschitz constant of the $p$-th-order derivative, $\mu$ is the strongly-convex parameter, and $D$ is the initial Bregman distance to the saddle point. Moreover, our line search scheme provably only requires an almost constant number of calls to a subproblem solver per iteration on average, making our first-order and second-order methods particularly amenable to implementation.

We consider several hill-climbing approaches to clustering as formulated by Fukunaga and Hostetler in the 1970's. We study both continuous-space and discrete-space (i.e., medoid) variants and establish their consistency.