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Reducing the cost and delay and improving quality are major issues for product and software development, especially in the automotive domain. Product line engineering is a wellknown approach to engineer systems with the aim to reduce costs and development time as well as to improve the product quality. Feature models enable to make logical selection of features and obtain a filtered set of assets that compose the product. We propose to use a color code in feature models to make possible decisions visual in the feature tree. The color code is explained and its use is illustrated. The completeness of the approach is discussed.

Sequential design of experiments for optimizing a reward function in causal systems can be effectively modeled by the sequential design of interventions in causal bandits (CBs). In the existing literature on CBs, a critical assumption is that the causal models remain constant over time. However, this assumption does not necessarily hold in complex systems, which constantly undergo temporal model fluctuations. This paper addresses the robustness of CBs to such model fluctuations. The focus is on causal systems with linear structural equation models (SEMs). The SEMs and the time-varying pre- and post-interventional statistical models are all unknown. Cumulative regret is adopted as the design criteria, based on which the objective is to design a sequence of interventions that incur the smallest cumulative regret with respect to an oracle aware of the entire causal model and its fluctuations. First, it is established that the existing approaches fail to maintain regret sub-linearity with even a few instances of model deviation. Specifically, when the number of instances with model deviation is as few as $T^\frac{1}{2L}$, where $T$ is the time horizon and $L$ is the longest causal path in the graph, the existing algorithms will have linear regret in $T$. Next, a robust CB algorithm is designed, and its regret is analyzed, where upper and information-theoretic lower bounds on the regret are established. Specifically, in a graph with $N$ nodes and maximum degree $d$, under a general measure of model deviation $C$, the cumulative regret is upper bounded by $\tilde{\mathcal{O}}(d^{L-\frac{1}{2}}(\sqrt{NT} + NC))$ and lower bounded by $\Omega(d^{\frac{L}{2}-2}\max\{\sqrt{T},d^2C\})$. Comparing these bounds establishes that the proposed algorithm achieves nearly optimal $\tilde{\mathcal{O}}(\sqrt{T})$ regret when $C$ is $o(\sqrt{T})$ and maintains sub-linear regret for a broader range of $C$.

The ability to remove features from the input of machine learning models is very important to understand and interpret model predictions. However, this is non-trivial for vision models since masking out parts of the input image typically causes large distribution shifts. This is because the baseline color used for masking (typically grey or black) is out of distribution. Furthermore, the shape of the mask itself can contain unwanted signals which can be used by the model for its predictions. Recently, there has been some progress in mitigating this issue (called missingness bias) in image masking for vision transformers. In this work, we propose a new masking method for CNNs we call layer masking in which the missingness bias caused by masking is reduced to a large extent. Intuitively, layer masking applies a mask to intermediate activation maps so that the model only processes the unmasked input. We show that our method (i) is able to eliminate or minimize the influence of the mask shape or color on the output of the model, and (ii) is much better than replacing the masked region by black or grey for input perturbation based interpretability techniques like LIME. Thus, layer masking is much less affected by missingness bias than other masking strategies. We also demonstrate how the shape of the mask may leak information about the class, thus affecting estimates of model reliance on class-relevant features derived from input masking. Furthermore, we discuss the role of data augmentation techniques for tackling this problem, and argue that they are not sufficient for preventing model reliance on mask shape. The code for this project is publicly available at //github.com/SriramB-98/layer_masking

We study the problem of communication-efficient distributed vector mean estimation, a commonly used subroutine in distributed optimization and Federated Learning (FL). Rand-$k$ sparsification is a commonly used technique to reduce communication cost, where each client sends $k < d$ of its coordinates to the server. However, Rand-$k$ is agnostic to any correlations, that might exist between clients in practical scenarios. The recently proposed Rand-$k$-Spatial estimator leverages the cross-client correlation information at the server to improve Rand-$k$'s performance. Yet, the performance of Rand-$k$-Spatial is suboptimal. We propose the Rand-Proj-Spatial estimator with a more flexible encoding-decoding procedure, which generalizes the encoding of Rand-$k$ by projecting the client vectors to a random $k$-dimensional subspace. We utilize Subsampled Randomized Hadamard Transform (SRHT) as the projection matrix and show that Rand-Proj-Spatial with SRHT outperforms Rand-$k$-Spatial, using the correlation information more efficiently. Furthermore, we propose an approach to incorporate varying degrees of correlation and suggest a practical variant of Rand-Proj-Spatial when the correlation information is not available to the server. Experiments on real-world distributed optimization tasks showcase the superior performance of Rand-Proj-Spatial compared to Rand-$k$-Spatial and other more sophisticated sparsification techniques.

For some hypothesis classes and input distributions, active agnostic learning needs exponentially fewer samples than passive learning; for other classes and distributions, it offers little to no improvement. The most popular algorithms for agnostic active learning express their performance in terms of a parameter called the disagreement coefficient, but it is known that these algorithms are inefficient on some inputs. We take a different approach to agnostic active learning, getting an algorithm that is competitive with the optimal algorithm for any binary hypothesis class $H$ and distribution $D_X$ over $X$. In particular, if any algorithm can use $m^*$ queries to get $O(\eta)$ error, then our algorithm uses $O(m^* \log |H|)$ queries to get $O(\eta)$ error. Our algorithm lies in the vein of the splitting-based approach of Dasgupta [2004], which gets a similar result for the realizable ($\eta = 0$) setting. We also show that it is NP-hard to do better than our algorithm's $O(\log |H|)$ overhead in general.

Motion planning is still an open problem for many disciplines, e.g., robotics, autonomous driving, due to their need for high computational resources that hinder real-time, efficient decision-making. A class of methods striving to provide smooth solutions is gradient-based trajectory optimization. However, those methods usually suffer from bad local minima, while for many settings, they may be inapplicable due to the absence of easy-to-access gradients of the optimization objectives. In response to these issues, we introduce Motion Planning via Optimal Transport (MPOT) -- a \textit{gradient-free} method that optimizes a batch of smooth trajectories over highly nonlinear costs, even for high-dimensional tasks, while imposing smoothness through a Gaussian Process dynamics prior via the planning-as-inference perspective. To facilitate batch trajectory optimization, we introduce an original zero-order and highly-parallelizable update rule -- -the Sinkhorn Step, which uses the regular polytope family for its search directions. Each regular polytope, centered on trajectory waypoints, serves as a local cost-probing neighborhood, acting as a \textit{trust region} where the Sinkhorn Step ``transports'' local waypoints toward low-cost regions. We theoretically show that Sinkhorn Step guides the optimizing parameters toward local minima regions of non-convex objective functions. We then show the efficiency of MPOT in a range of problems from low-dimensional point-mass navigation to high-dimensional whole-body robot motion planning, evincing its superiority compared to popular motion planners, paving the way for new applications of optimal transport in motion planning.

Optimal transportation is a fundamental topic that has attracted a great amount of attention from machine learning community in the past decades. In this paper, we consider an interesting discrete dynamic optimal transport problem: can we efficiently update the optimal transport plan when the weights or the locations of the data points change? This problem is naturally motivated by several applications in machine learning. For example, we often need to compute the optimal transportation cost between two different data sets; if some change happens to a few data points, should we re-compute the high complexity cost function or update the cost by some efficient dynamic data structure? We are aware that several dynamic maximum flow algorithms have been proposed before, however, the research on dynamic minimum cost flow problem is still quite limited, to the best of our knowledge. We propose a novel 2D Skip Orthogonal List together with some dynamic tree techniques. Although our algorithm is based on the conventional simplex method, it can efficiently complete each pivoting operation within $O(|V|)$ time with high probability where $V$ is the set of all supply and demand nodes. Since dynamic modifications typically do not introduce significant changes, our algorithm requires only a few simplex iterations in practice. So our algorithm is more efficient than re-computing the optimal transportation cost that needs at least one traversal over all the $O(|E|) = O(|V|^2)$ variables in general cases. Our experiments demonstrate that our algorithm significantly outperforms existing algorithms in the dynamic scenarios.

Computational simulation is increasingly relied upon for high-consequence engineering decisions, and a foundational element to solid mechanics simulations, such as finite element analysis (FEA), is a credible constitutive or material model. Calibration of these complex models is an essential step; however, the selection, calibration and validation of material models is often a discrete, multi-stage process that is decoupled from material characterization activities, which means the data collected does not always align with the data that is needed. To address this issue, an integrated workflow for delivering an enhanced characterization and calibration procedure (Interlaced Characterization and Calibration (ICC)) is introduced. This framework leverages Bayesian optimal experimental design (BOED) to select the optimal load path for a cruciform specimen in order to collect the most informative data for model calibration. The critical first piece of algorithm development is to demonstrate the active experimental design for a fast model with simulated data. For this demonstration, a material point simulator that models a plane stress elastoplastic material subject to bi-axial loading was chosen. The ICC framework is demonstrated on two exemplar problems in which BOED is used to determine which load step to take, e.g., in which direction to increment the strain, at each iteration of the characterization and calibration cycle. Calibration results from data obtained by adaptively selecting the load path within the ICC algorithm are compared to results from data generated under two naive static load paths that were chosen a priori based on human intuition. In these exemplar problems, data generated in an adaptive setting resulted in calibrated model parameters with reduced measures of uncertainty compared to the static settings.

Causality can be described in terms of a structural causal model (SCM) that carries information on the variables of interest and their mechanistic relations. For most processes of interest the underlying SCM will only be partially observable, thus causal inference tries to leverage any exposed information. Graph neural networks (GNN) as universal approximators on structured input pose a viable candidate for causal learning, suggesting a tighter integration with SCM. To this effect we present a theoretical analysis from first principles that establishes a novel connection between GNN and SCM while providing an extended view on general neural-causal models. We then establish a new model class for GNN-based causal inference that is necessary and sufficient for causal effect identification. Our empirical illustration on simulations and standard benchmarks validate our theoretical proofs.

Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such a graph-structure is available. In practice, however, real-world graphs are often noisy and incomplete or might not be available at all. With this work, we propose to jointly learn the graph structure and the parameters of graph convolutional networks (GCNs) by approximately solving a bilevel program that learns a discrete probability distribution on the edges of the graph. This allows one to apply GCNs not only in scenarios where the given graph is incomplete or corrupted but also in those where a graph is not available. We conduct a series of experiments that analyze the behavior of the proposed method and demonstrate that it outperforms related methods by a significant margin.