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2. Progressive participation

   https://doi.org/10.3982/TE4636  

   Bergemann, Dirk; Strack, Philipp (January 2022, Theoretical Economics)

   A single seller faces a sequence of buyers with unit demand. The buyers are forward‐looking and long‐lived. Each buyer has private information about his arrival time and valuation where the latter evolves according to a geometric Brownian motion. Any incentive‐compatible mechanism has to induce truth‐telling about the arrival time and the evolution of the valuation. We establish that the optimal stationary allocation policy can be implemented by a simple posted price. The truth‐telling constraint regarding the arrival time can be represented as an optimal stopping problem that determines the first time at which the buyer participates in the mechanism. The optimal mechanism thus induces progressive participation by each buyer: he either participates immediately or at a future random time. 

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3. Efficient and effective ER with progressive blocking

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4. Efficient and Effective ER with Progressive Blocking

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5. EXPLANATION BY PROGRESSIVE EXAGGERATION

   Sumedha Singla, Brian Pollack (January 2020, The International Conference on Learning Representations)

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   As machine learning methods see greater adoption and implementation in high-stakes applications such as medical image diagnosis, the need for model interpretability and explanation has become more critical. Classical approaches that assess feature importance (e.g., saliency maps) do not explain how and why a particular region of an image is relevant to the prediction. We propose a method that explains the outcome of a classification black-box by gradually exaggerating the semantic effect of a given class. Given a query input to a classifier, our method produces a progressive set of plausible variations of that query, which gradually changes the posterior probability from its original class to its negation. These counter-factually generated samples preserve features unrelated to the classification decision, such that a user can employ our method as a “tuning knob” to traverse a data manifold while crossing the decision boundary. Our method is model agnostic and only requires the output value and gradient of the predictor with respect to its input. 

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