Understanding PAC-Bayes and Overfitting
PAC Bayes helps explain overfitting by shifting the perspective from “how large is the hypothesis space?” to “how simple/compressible are the specific solutions the model is likely to pick under a prior?” The paper st...
PAC Bayes helps explain overfitting by shifting the perspective from “how large is the hypothesis space?” to “how simple/compressible are the specific solutions the model is likely to pick under a prior?” The paper states that frameworks like PAC Bayes (and related countable hypothesis bounds) rigorously characterize generalization behaviour that includes benign overfitting rather than requiring rethinking generalization. [:cite[2]{ln=2}], [:cite[1]{ln=4}], [:cite[3]{ln=1}] It emphasizes that these frameworks base generalization on which hypotheses are likely under a prior (rather than penalizing the overall size of the hypothesis class), and notes that they do not penalize models simply for being able to fit noise , which is exactly the regime associated with benign overfitting. [:cite[4]{ln=1}], [e c69 2], [:cite[5]{ln=4}] Concretely, it describes the PAC Bayes type interpretation as: “Expected Risk ≤ Empirical Risk + Model Compressibility.” This links overfitting risk to whether the fitted solution is compressible/simple enough, even if it fits the training data very closely (including noise). [:cite[6]{ln=5}], [:cite[7]{ln=2}] The paper ties this to the idea of soft inductive biases : instead of restricting the hypothesis space with “restriction biases” (hardly preventing overfitting), PAC Bayes supports a flexible hypothesis space together with a prior preference for simpler solutions consistent with the data —yielding non vacuous guarantees in overfitting like settings. [:cite[9]{ln=1} ?], [:cite[8]{ln=2}], [:cite[11]{ln=2}], [:cite[10]{ln=2}] In short: PAC Bayes plays a role in understanding overfitting by providing non vacuous generalization bounds whenever the overfitting solutions are still likely under the prior , i.e., when they admit a notion of compression/simplicity that prevents that overfitting from being “harmful” for test performance. [:cite[6]{ln=5}], [:cite[12]{ln=2}], [:cite[4]{ln=1}].