Random sample consensus (RANSAC) is a successful algorithm in model fitting applications. It is vital to have strong exploration phase when there are an enormous amount of outliers within the dataset. Achieving a proper model is guaranteed by pure exploration strategy of RANSAC. However, finding the optimum result requires exploitation. GASAC is an evolutionary paradigm to add exploitation capability to the algorithm. Although GASAC improves the results of RANSAC, it has a fixed strategy for balancing between exploration and exploitation. In this paper, a new paradigm is proposed based on genetic algorithm with an adaptive strategy. We utilize an adaptive genetic operator to select high fitness individuals as parents and mutate low fitness ones. In the mutation phase, a training method is used to gradually learn which gene is the best replacement for the mutated gene. The proposed method adaptively balance between exploration and exploitation by learning about genes. During the final Iterations, the algorithm draws on this information to improve the final results. The proposed method is extensively evaluated on two set of experiments. In all tests, our method outperformed the other methods in terms of both the number of inliers found and the speed of the algorithm.
Bail-out test @cite_1 is another paradigm to terminate the verification early which is similar to R-RANSAC @cite_9 . More specifically, it considers the number of inliers @math within @math which is a subset of all points @math follows a hyper-geometric distribution @math ,where @math is number of inliers for @math , @math total number of points in @math , and @math size of @math . It considers @math inlier count for the best current model and if the probability of @math is below a given threshold, the verification can continue.
@cite_9 @cite_1
2207085776 2950162031 2542071751 1523041988
Robust estimation of model parameters in the presence of outliers is a key problem in computer vision. RANSAC inspired techniques are widely used in this context, although their application might be limited due to the need of a priori knowledge on the inlier noise level. We propose a new approach for jointly optimizing over model parameters and the inlier noise level based on the likelihood ratio test. This allows control over the type I error incurred. We also propose an early bailout strategy for efficiency. Tests on both synthetic and real data show that our method outperforms the state-of-the-art in a fraction of the time. We investigate the clustering performances of the relaxed @math means in the setting of sub-Gaussian Mixture Model (sGMM) and Stochastic Block Model (SBM). After identifying the appropriate signal-to-noise ratio (SNR), we prove that the misclassification error decay exponentially fast with respect to this SNR. These partial recovery bounds for the relaxed @math means improve upon results currently known in the sGMM setting. In the SBM setting, applying the relaxed @math means SDP allows to handle general connection probabilities whereas other SDPs investigated in the literature are restricted to the assortative case (where within group probabilities are larger than between group probabilities). Again, this partial recovery bound complements the state-of-the-art results. All together, these results put forward the versatility of the relaxed @math means. Motivated by online recommendation and advertising systems, we consider a causal model for stochastic contextual bandits with a latent low-dimensional confounder. In our model, there are @math observed contexts and @math arms of the bandit. The observed context influences the reward obtained through a latent confounder variable with cardinality @math ( @math ). The arm choice and the latent confounder causally determines the reward while the observed context is correlated with the confounder. Under this model, the @math mean reward matrix @math (for each context in @math and each arm in @math ) factorizes into non-negative factors @math ( @math ) and @math ( @math ). This insight enables us to propose an @math -greedy NMF-Bandit algorithm that designs a sequence of interventions (selecting specific arms), that achieves a balance between learning this low-dimensional structure and selecting the best arm to minimize regret. Our algorithm achieves a regret of @math at time @math , as compared to @math for conventional contextual bandits, assuming a constant gap between the best arm and the rest for each context. These guarantees are obtained under mild sufficiency conditions on the factors that are weaker versions of the well-known Statistical RIP condition. We further propose a class of generative models that satisfy our sufficient conditions, and derive a lower bound of @math . These are the first regret guarantees for online matrix completion with bandit feedback, when the rank is greater than one. We further compare the performance of our algorithm with the state of the art, on synthetic and real world data-sets. A traditional counterexample to a linear-time safety property shows the values of all signals at all times prior to the error. However, some signals may not be critical to causing the failure. A succinct explanation may help human understanding as well as speed up algorithms that have to analyze many such traces. In Bounded Model Checking (BMC), a counterexample is constructed from a satisfying assignment to a Boolean formula, typically in CNF. Modern SAT solvers usually assign values to all variables when the input formula is satisfiable. Deriving minimal satisfying assignments from such complete assignments does not lead to concise explanations of counterexamples because of how CNF formulae are derived from the models. Hence, we formulate the extraction of a succinct counterexample as the problem of finding a minimal assignment that, together with the Boolean formula describing the model, implies an objective. We present a two-stage algorithm for this problem, such that the result of each stage contributes to identify the “interesting” events that cause the failure. We demonstrate the effectiveness of our approach with an example and with experimental results.