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Current approaches rely on simple augmentation methods to generate pseudo anomalies that replicate unseen anomalies. Despite being promising in image data, these methods are found to be ineffective in time series data due to the failure to preserve its sequential nature, resulting in trivial or unrealistic anomaly patterns. They are further plagued when the training data is contaminated with unlabeled anomalies. This work introduces $\\textbf{IMPACT}$, a novel framework that leverages $\\underline{\\textbf{i}}$nfluence $\\underline{\\textbf{m}}$odeling for o$\\underline{\\textbf{p}}$en-set time series $\\underline{\\textbf{a}}$nomaly dete$\\underline{\\textbf{ct}}$ion, to tackle these challenges. 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This work introduces $\\textbf{IMPACT}$, a novel framework that leverages $\\underline{\\textbf{i}}$nfluence $\\underline{\\textbf{m}}$odeling for o$\\underline{\\textbf{p}}$en-set time series $\\underline{\\textbf{a}}$nomaly dete$\\underline{\\textbf{ct}}$ion, to tackle these challenges. 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