In recent years, the usage of ensemble learning in applications has grown significantly due to increasing computational power allowing the training of large ensembles in reasonable time frames. Many applications, e.g., malware detection, face recognition, or financial decision-making, use a finite set of learning algorithms and do aggregate them in a way that a better predictive performance is obtained than any other of the individual learning algorithms. In the field of Post-Silicon Validation for semiconductor devices (PSV), data sets are typically provided that consist of various devices like, e.g., chips of different manufacturing lines. In PSV, the task is to approximate the underlying function of the data with multiple learning algorithms, each trained on a device-specific subset, instead of improving the performance of arbitrary classifiers on the entire data set. Furthermore, the expectation is that an unknown number of subsets describe functions showing very different characteristics. Corresponding ensemble members, which are called outliers, can heavily influence the approximation. Our method aims to find a suitable approximation that is robust to outliers and represents the best or worst case in a way that will apply to as many types as possible. A 'soft-max' or 'soft-min' function is used in place of a maximum or minimum operator. A Neural Network (NN) is trained to learn this 'soft-function' in a two-stage process. First, we select a subset of ensemble members that is representative of the best or worst case. Second, we combine these members and define a weighting that uses the properties of the Local Outlier Factor (LOF) to increase the influence of non-outliers and to decrease outliers. The weighting ensures robustness to outliers and makes sure that approximations are suitable for most types.
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This manuscript proposes to extend the information set of time-series regression trees with latent stationary factors extracted via state-space methods. In doing so, this approach generalises time-series regression trees on two dimensions. First, it allows to handle predictors that exhibit measurement error, non-stationary trends, seasonality and/or irregularities such as missing observations. Second, it gives a transparent way for using domain-specific theory to inform time-series regression trees. As a byproduct, this technique sets the foundations for structuring powerful ensembles. Their real-world applicability is studied under the lenses of empirical macro-finance.
In many machine learning tasks, a common approach for dealing with large-scale data is to build a small summary, {\em e.g.,} coreset, that can efficiently represent the original input. However, real-world datasets usually contain outliers and most existing coreset construction methods are not resilient against outliers (in particular, an outlier can be located arbitrarily in the space by an adversarial attacker). In this paper, we propose a novel robust coreset method for the {\em continuous-and-bounded learning} problems (with outliers) which includes a broad range of popular optimization objectives in machine learning, {\em e.g.,} logistic regression and $ k $-means clustering. Moreover, our robust coreset can be efficiently maintained in fully-dynamic environment. To the best of our knowledge, this is the first robust and fully-dynamic coreset construction method for these optimization problems. Another highlight is that our coreset size can depend on the doubling dimension of the parameter space, rather than the VC dimension of the objective function which could be very large or even challenging to compute. Finally, we conduct the experiments on real-world datasets to evaluate the effectiveness of our proposed robust coreset method.
An informative measurement is the most efficient way to gain information about an unknown state. We give a first-principles derivation of a general-purpose dynamic programming algorithm that returns an optimal sequence of informative measurements by sequentially maximizing the entropy of possible measurement outcomes. This algorithm can be used by an autonomous agent or robot to decide where best to measure next, planning a path corresponding to an optimal sequence of informative measurements. The algorithm is applicable to states and controls that are continuous or discrete, and agent dynamics that is either stochastic or deterministic; including Markov decision processes and Gaussian processes. Recent results from approximate dynamic programming and reinforcement learning, including on-line approximations such as rollout and Monte Carlo tree search, allow the measurement task to be solved in real-time. The resulting solutions include non-myopic paths and measurement sequences that can generally outperform, sometimes substantially, commonly used greedy approaches. This is demonstrated for a global search problem, where on-line planning with an extended local search is found to reduce the number of measurements in the search by approximately half. A variant of the algorithm is derived for Gaussian processes for active sensing.
We introduce a novel method for clustering using a semidefinite programming (SDP) relaxation of the Max k-Cut problem. The approach is based on a new methodology for rounding the solution of an SDP relaxation using iterated linear optimization. We show the vertices of the Max k-Cut SDP relaxation correspond to partitions of the data into at most k sets. We also show the vertices are attractive fixed points of iterated linear optimization. Each step of this iterative procedure solves a relaxation of the closest vertex problem and leads to a new clustering problem where the underlying clusters are more clearly defined. Our experiments show that using fixed point iteration for rounding the Max k-Cut SDP relaxation leads to significantly better results when compared to randomized rounding.
We prove upper and lower bounds on the minimal spherical dispersion, improving upon previous estimates obtained by Rote and Tichy [Spherical dispersion with an application to polygonal approximation of curves, Anz. \"Osterreich. Akad. Wiss. Math.-Natur. Kl. 132 (1995), 3--10]. In particular, we see that the inverse $N(\varepsilon,d)$ of the minimal spherical dispersion is, for fixed $\varepsilon>0$, linear in the dimension $d$ of the ambient space. We also derive upper and lower bounds on the expected dispersion for points chosen independently and uniformly at random from the Euclidean unit sphere. In terms of the corresponding inverse $\widetilde{N}(\varepsilon,d)$, our bounds are optimal with respect to the dependence on $\varepsilon$.
Logistic Bandits have recently undergone careful scrutiny by virtue of their combined theoretical and practical relevance. This research effort delivered statistically efficient algorithms, improving the regret of previous strategies by exponentially large factors. Such algorithms are however strikingly costly as they require $\Omega(t)$ operations at each round. On the other hand, a different line of research focused on computational efficiency ($\mathcal{O}(1)$ per-round cost), but at the cost of letting go of the aforementioned exponential improvements. Obtaining the best of both world is unfortunately not a matter of marrying both approaches. Instead we introduce a new learning procedure for Logistic Bandits. It yields confidence sets which sufficient statistics can be easily maintained online without sacrificing statistical tightness. Combined with efficient planning mechanisms we design fast algorithms which regret performance still match the problem-dependent lower-bound of Abeille et al. (2021). To the best of our knowledge, those are the first Logistic Bandit algorithms that simultaneously enjoy statistical and computational efficiency.
Perturbations targeting the graph structure have proven to be extremely effective in reducing the performance of Graph Neural Networks (GNNs), and traditional defenses such as adversarial training do not seem to be able to improve robustness. This work is motivated by the observation that adversarially injected edges effectively can be viewed as additional samples to a node's neighborhood aggregation function, which results in distorted aggregations accumulating over the layers. Conventional GNN aggregation functions, such as a sum or mean, can be distorted arbitrarily by a single outlier. We propose a robust aggregation function motivated by the field of robust statistics. Our approach exhibits the largest possible breakdown point of 0.5, which means that the bias of the aggregation is bounded as long as the fraction of adversarial edges of a node is less than 50\%. Our novel aggregation function, Soft Medoid, is a fully differentiable generalization of the Medoid and therefore lends itself well for end-to-end deep learning. Equipping a GNN with our aggregation improves the robustness with respect to structure perturbations on Cora ML by a factor of 3 (and 5.5 on Citeseer) and by a factor of 8 for low-degree nodes.
This paper addresses the problem of formally verifying desirable properties of neural networks, i.e., obtaining provable guarantees that neural networks satisfy specifications relating their inputs and outputs (robustness to bounded norm adversarial perturbations, for example). Most previous work on this topic was limited in its applicability by the size of the network, network architecture and the complexity of properties to be verified. In contrast, our framework applies to a general class of activation functions and specifications on neural network inputs and outputs. We formulate verification as an optimization problem (seeking to find the largest violation of the specification) and solve a Lagrangian relaxation of the optimization problem to obtain an upper bound on the worst case violation of the specification being verified. Our approach is anytime i.e. it can be stopped at any time and a valid bound on the maximum violation can be obtained. We develop specialized verification algorithms with provable tightness guarantees under special assumptions and demonstrate the practical significance of our general verification approach on a variety of verification tasks.
Recently, ensemble has been applied to deep metric learning to yield state-of-the-art results. Deep metric learning aims to learn deep neural networks for feature embeddings, distances of which satisfy given constraint. In deep metric learning, ensemble takes average of distances learned by multiple learners. As one important aspect of ensemble, the learners should be diverse in their feature embeddings. To this end, we propose an attention-based ensemble, which uses multiple attention masks, so that each learner can attend to different parts of the object. We also propose a divergence loss, which encourages diversity among the learners. The proposed method is applied to the standard benchmarks of deep metric learning and experimental results show that it outperforms the state-of-the-art methods by a significant margin on image retrieval tasks.
In this paper, we study the optimal convergence rate for distributed convex optimization problems in networks. We model the communication restrictions imposed by the network as a set of affine constraints and provide optimal complexity bounds for four different setups, namely: the function $F(\xb) \triangleq \sum_{i=1}^{m}f_i(\xb)$ is strongly convex and smooth, either strongly convex or smooth or just convex. Our results show that Nesterov's accelerated gradient descent on the dual problem can be executed in a distributed manner and obtains the same optimal rates as in the centralized version of the problem (up to constant or logarithmic factors) with an additional cost related to the spectral gap of the interaction matrix. Finally, we discuss some extensions to the proposed setup such as proximal friendly functions, time-varying graphs, improvement of the condition numbers.
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