{
  "id": "2205.12940",
  "version": "v1",
  "published": "2022-05-25T17:45:04.000Z",
  "updated": "2022-05-25T17:45:04.000Z",
  "title": "Conformal Prediction Intervals with Temporal Dependence",
  "authors": [
    "Zhen Lin",
    "Shubhendu Trivedi",
    "Jimeng Sun"
  ],
  "comment": "15 pages (main paper, including references) + 4 pages (supplementary material)",
  "categories": [
    "stat.ML",
    "cs.LG",
    "stat.ME"
  ],
  "abstract": "Cross-sectional prediction is common in many domains such as healthcare, including forecasting tasks using electronic health records, where different patients form a cross-section. We focus on the task of constructing valid prediction intervals (PIs) in time-series regression with a cross-section. A prediction interval is considered valid if it covers the true response with (a pre-specified) high probability. We first distinguish between two notions of validity in such a setting: cross-sectional and longitudinal. Cross-sectional validity is concerned with validity across the cross-section of the time series data, while longitudinal validity accounts for the temporal dimension. Coverage guarantees along both these dimensions are ideally desirable; however, we show that distribution-free longitudinal validity is theoretically impossible. Despite this limitation, we propose Conformal Prediction with Temporal Dependence (CPTD), a procedure which is able to maintain strict cross-sectional validity while improving longitudinal coverage. CPTD is post-hoc and light-weight, and can easily be used in conjunction with any prediction model as long as a calibration set is available. We focus on neural networks due to their ability to model complicated data such as diagnosis codes for time-series regression, and perform extensive experimental validation to verify the efficacy of our approach. We find that CPTD outperforms baselines on a variety of datasets by improving longitudinal coverage and often providing more efficient (narrower) PIs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-25T17:45:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conformal prediction intervals",
      "temporal dependence",
      "improving longitudinal coverage",
      "time-series regression",
      "maintain strict cross-sectional validity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}