Graph data is ubiquitous in academia and industry, from social networks to bioinformatics. The pervasiveness of graphs today has raised the demand for algorithms that can answer various questions: Which products would a user like to purchase given her order list? Which users are buying fake followers to increase their public reputation? Myriads of new graph mining algorithms are proposed every year to answer such questions - each with a distinct problem formulation, computational time, and memory footprint. This lack of unity makes it difficult for a practitioner to compare different algorithms and pick the most suitable one for a specific application. These challenges - even more severe for non-experts - create a gap in which state-of-the-art techniques developed in academic settings fail to be optimally deployed in real-world applications. To bridge this gap, we propose AUTOGM, an automated system for graph mining algorithm development. We first define a unified framework UNIFIEDGM that integrates various message-passing based graph algorithms, ranging from conventional algorithms like PageRank to graph neural networks. Then UNIFIEDGM defines a search space in which five parameters are required to determine a graph algorithm. Under this search space, AUTOGM explicitly optimizes for the optimal parameter set of UNIFIEDGM using Bayesian Optimization. AUTOGM defines a novel budget-aware objective function for the optimization to incorporate a practical issue - finding the best speed-accuracy trade-off under a computation budget - into the graph algorithm generation problem. Experiments on real-world benchmark datasets demonstrate that AUTOGM generates novel graph mining algorithms with the best speed/accuracy trade-off compared to existing models with heuristic parameters.

Cable trees are widely used in industrial products to transmit energy and information between different product parts. For example, cable trees are needed in cars to automate many previously mechanical functions such as moving seats or opening windows and to add new functions such as a voice-controlled navigation or an onboard entertainment system. It is thus not surprising that for example a car like the VW Golf 7 contains 14 cable trees with a total of 1633 cables. The manufacturing of cable trees usually relies on cheap manual labour performed in low-cost countries where humans plug cables into harnesses following a wiring plan. Only few automated manufacturing solutions exist, which rely on complex robotic machines. These machines execute a sequence of wiring operations that highly qualified technicians develop by analyzing the wiring plan. With the continuing tendency towards customer-specific and resource-efficient justin-time manufacturing, smaller batch sizes of cable trees need to be manufactured requiring a frequent change of wiring plans, for which wiring sequences should be derived instantly. Scaling up human expertise to such frequent changes is simply impossible, which explains a growing interest in the intelligent automated manufacturing of cable trees. This interest is also nourished by a further miniaturization of cable harnesses, which will make their manual manufacturing impossible.

We introduce Constr-DRKM, a deep kernel method for the unsupervised learning of disentangled data representations. We propose augmenting the original deep restricted kernel machine formulation for kernel PCA by orthogonality constraints on the latent variables to promote disentanglement and to make it possible to carry out optimization without first defining a stabilized objective. After illustrating an end-to-end training procedure based on a quadratic penalty optimization algorithm with warm start, we quantitatively evaluate the proposed method's effectiveness in disentangled feature learning. We demonstrate on four benchmark datasets that this approach performs similarly overall to $\beta$-VAE on a number of disentanglement metrics when few training points are available, while being less sensitive to randomness and hyperparameter selection than $\beta$-VAE. We also present a deterministic initialization of Constr-DRKM's training algorithm that significantly improves the reproducibility of the results. Finally, we empirically evaluate and discuss the role of the number of layers in the proposed methodology, examining the influence of each principal component in every layer and showing that components in lower layers act as local feature detectors capturing the broad trends of the data distribution, while components in deeper layers use the representation learned by previous layers and more accurately reproduce higher-level features.

Bayesian optimization is a popular method for solving the problem of global optimization of an expensive-to-evaluate black-box function. It relies on a probabilistic surrogate model of the objective function, upon which an acquisition function is built to determine where next to evaluate the objective function. In general, Bayesian optimization with Gaussian process regression operates on a continuous space. When input variables are categorical or discrete, an extra care is needed. A common approach is to use one-hot encoded or Boolean representation for categorical variables which might yield a {\em combinatorial explosion} problem. In this paper we present a method for Bayesian optimization in a combinatorial space, which can operate well in a large combinatorial space. The main idea is to use a random mapping which embeds the combinatorial space into a convex polytope in a continuous space, on which all essential process is performed to determine a solution to the black-box optimization in the combinatorial space. We describe our {\em combinatorial Bayesian optimization} algorithm and present its regret analysis. Numerical experiments demonstrate that our method outperforms existing methods.

This paper presents redundancy resolution and disturbance rejection via torque optimization in Hybrid Cable-Driven Robots (HCDRs). To begin with, we initiate a redundant HCDR for nonlinear whole-body system modeling and model reduction. Based on the reduced dynamic model, two new methods are proposed to solve the redundancy resolution problem: joint-space torque optimization for actuated joints (TOAJ) and joint-space torque optimization for actuated and unactuated joints (TOAUJ), and they can be extended to other HCDRs. Compared to the existing approaches, this paper provides the first solution (TOAUJ-based method) for HCDRs that can solve the redundancy resolution problem as well as disturbance rejection. Additionally, this paper develops detailed algorithms targeting TOAJ and TOAUJ implementation. A simple yet effective controller is designed for generated data analysis and validation. Case studies are conducted to evaluate the performance of TOAJ and TOAUJ, and the results suggest the effectiveness of the aforementioned approaches.

Bayesian optimization (BO) is a popular method to optimize expensive black-box functions. It efficiently tunes machine learning algorithms under the implicit assumption that hyperparameter evaluations cost approximately the same. In reality, the cost of evaluating different hyperparameters, be it in terms of time, dollars or energy, can span several orders of magnitude of difference. While a number of heuristics have been proposed to make BO cost-aware, none of these have been proven to work robustly. In this work, we reformulate cost-aware BO in terms of Pareto efficiency and introduce the cost Pareto Front, a mathematical object allowing us to highlight the shortcomings of commonly used acquisition functions. Based on this, we propose a novel Pareto-efficient adaptation of the expected improvement. On 144 real-world black-box function optimization problems we show that our Pareto-efficient acquisition functions significantly outperform previous solutions, bringing up to 50% speed-ups while providing finer control over the cost-accuracy trade-off. We also revisit the common choice of Gaussian process cost models, showing that simple, low-variance cost models predict training times effectively.

Barren plateau landscapes correspond to gradients that vanish exponentially in the number of qubits. Such landscapes have been demonstrated for variational quantum algorithms and quantum neural networks with either deep circuits or global cost functions. For obvious reasons, it is expected that gradient-based optimizers will be significantly affected by barren plateaus. However, whether or not gradient-free optimizers are impacted is a topic of debate, with some arguing that gradient-free approaches are unaffected by barren plateaus. Here we show that, indeed, gradient-free optimizers do not solve the barren plateau problem. Our main result proves that cost function differences, which are the basis for making decisions in a gradient-free optimization, are exponentially suppressed in a barren plateau. Hence, without exponential precision, gradient-free optimizers will not make progress in the optimization. We numerically confirm this by training in a barren plateau with several gradient-free optimizers (Nelder-Mead, Powell, and COBYLA algorithms), and show that the numbers of shots required in the optimization grows exponentially with the number of qubits.

We estimate the general influence functions for spatio-temporal Hawkes processes using a tensor recovery approach by formulating the location dependent influence function that captures the influence of historical events as a tensor kernel. We assume a low-rank structure for the tensor kernel and cast the estimation problem as a convex optimization problem using the Fourier transformed nuclear norm (TNN). We provide theoretical performance guarantees for our approach and present an algorithm to solve the optimization problem. We demonstrate the efficiency of our estimation with numerical simulations.

Nonnegative least squares (NNLS) problems arise in models that rely on additive linear combinations. In particular, they are at the core of nonnegative matrix factorization (NMF) algorithms. The nonnegativity constraint is known to naturally favor sparsity, that is, solutions with few non-zero entries. However, it is often useful to further enhance this sparsity, as it improves the interpretability of the results and helps reducing noise. While the $\ell_0$-"norm", equal to the number of non-zeros entries in a vector, is a natural sparsity measure, its combinatorial nature makes it difficult to use in practical optimization schemes. Most existing approaches thus rely either on its convex surrogate, the $\ell_1$-norm, or on heuristics such as greedy algorithms. In the case of multiple right-hand sides NNLS (MNNLS), which are used within NMF algorithms, sparsity is often enforced column- or row-wise, and the fact that the solution is a matrix is not exploited. In this paper, we first introduce a novel formulation for sparse MNNLS, with a matrix-wise $\ell_0$ sparsity constraint. Then, we present a two-step algorithm to tackle this problem. The first step uses a homotopy algorithm to produce the whole regularization path for all the $\ell_1$-penalized NNLS problems arising in MNNLS, that is, to produce a set of solutions representing different tradeoffs between reconstruction error and sparsity. The second step selects solutions among these paths in order to build a sparsity-constrained matrix that minimizes the reconstruction error. We illustrate the advantages of our proposed algorithm for the unmixing of facial and hyperspectral images.

Sequential assembly with geometric primitives has drawn attention in robotics and 3D vision since it yields a practical blueprint to construct a target shape. However, due to its combinatorial property, a greedy method falls short of generating a sequence of volumetric primitives. To alleviate this consequence induced by a huge number of feasible combinations, we propose a combinatorial 3D shape generation framework. The proposed framework reflects an important aspect of human generation processes in real life -- we often create a 3D shape by sequentially assembling unit primitives with geometric constraints. To find the desired combination regarding combination evaluations, we adopt Bayesian optimization, which is able to exploit and explore efficiently the feasible regions constrained by the current primitive placements. An evaluation function conveys global structure guidance for an assembly process and stability in terms of gravity and external forces simultaneously. Experimental results demonstrate that our method successfully generates combinatorial 3D shapes and simulates more realistic generation processes. We also introduce a new dataset for combinatorial 3D shape generation. All the codes are available at \url{https://github.com/POSTECH-CVLab/Combinatorial-3D-Shape-Generation}.