    \begin{algorithmic}[1]
        \State $\beta \gets \beta^*$ \Comment{load best set of parameters for BidNet}
        \State $\alpha \gets \alpha^*$ \Comment{load optimized set of parameters for synthesizer}
        \State $\tilde{\mathbf{c}}\sim A_{\alpha^*}(\mathbf{z})$\Comment{sample synthetic examples from the trained synthesizer}
        \State $\mathbf{c} \sim D_{test}$\Comment{sample a test-set of real instances}
        \State $\hat{b} \sim B_{\beta^*}(\mathbf{c})$\Comment{sample predicted bids from the test-set of real instances using BidNet}
        \State $\tilde{b} \sim B_{\beta^*}(\tilde{\mathbf{c}})$\Comment{sample fake bids with the synthetic data emanating from the synthesizer}
        \State $Dist(p(b) || p(\tilde{b}))$\Comment{compute the statistical distance between the fake and real distributions of bids}
        \State $Dist(p(b) || p(\hat{b}))$\Comment{compute the statistical distance between the predicted and real distributions of bids}
        \State $Dist(p(\hat{b}) || p(\tilde{b}))$\Comment{compute the statistical distance between the predicted and fake distributions of bids}
    \end{algorithmic}

\begin{algorithmic}
[1]
\State $\beta \gets \beta^*$ \Comment{load best set of parameters for BidNet}
\State $\alpha \gets \alpha^*$ \Comment{load optimized set of parameters for synthesizer}
\State $\tilde{\mathbf{c}}\sim A_{\alpha^*}(\mathbf{z})$\Comment{sample synthetic examples from the trained synthesizer}
\State $\mathbf{c} \sim D_{test}$\Comment{sample a test-set of real instances}
\State $\hat{b} \sim B_{\beta^*}(\mathbf{c})$\Comment{sample predicted bids from the test-set of real instances using BidNet}
\State $\tilde{b} \sim B_{\beta^*}(\tilde{\mathbf{c}})$\Comment{sample fake bids with the synthetic data emanating from the synthesizer}
\State $Dist(p(b) || p(\tilde{b}))$\Comment{compute the statistical distance between the fake and real distributions of bids}
\State $Dist(p(b) || p(\hat{b}))$\Comment{compute the statistical distance between the predicted and real distributions of bids}
\State $Dist(p(\hat{b}) || p(\tilde{b}))$\Comment{compute the statistical distance between the predicted and fake distributions of bids}
\end{algorithmic}
{
    "title": "implementing a hierarchical deep learning approach for simulating   multi-level auction data",
    "id": "2207.12255",
    "abstract": "we present a deep learning solution to address the challenges of simulating realistic synthetic first-price sealed-bid auction data. the complexities encountered in this type of auction data include high-cardinality discrete feature spaces and a multilevel structure arising from multiple bids associated with a single auction instance. our methodology combines deep generative modeling (dgm) with an artificial learner that predicts the conditional bid distribution based on auction characteristics, contributing to advancements in simulation-based research. this approach lays the groundwork for creating realistic auction environments suitable for agent-based learning and modeling applications. our contribution is twofold: we introduce a comprehensive methodology for simulating multilevel discrete auction data, and we underscore the potential of dgm as a powerful instrument for refining simulation techniques and fostering the development of economic models grounded in generative ai.",
    "categories": "econ.gn q-fin.ec",
    "doi": "",
    "created": "2022-07-25",
    "updated": "2024-02-15",
    "authors": [
        "igor sadoune",
        "andrea lodi",
        "marcelin joanis"
    ],
    "affiliation": [],
    "url": "https://arxiv.org/abs/2207.12255"
}
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