Conditionally Strongly Log-Concave Generative Models
Conditionally Strongly Log-Concave Generative Models
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DOI：
10.48550/arxiv.2306.00181
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发表时间：
2023-05
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影响因子：
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通讯作者：
Florentin Guth;Etienne Lempereur;Joan Bruna;S. Mallat
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文献类型：
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作者：
Florentin Guth;Etienne Lempereur;Joan Bruna;S. Mallat
深度图像生成模型的令人印象深刻的结果与提供理论保证的经典算法之间的差距越来越大。前者遭受模式崩溃或记忆问题，限制了它们对科学数据的应用。后者需要限制性的假设，如对数，以逃避维数灾难。我们通过引入条件强对数凹（CSLC）模型部分弥合了这一差距，该模型将数据分布分解为强对数凹的条件概率分布的乘积。这种因式分解是用适合于数据分布的正交投影仪获得的。它导致有效的参数估计和采样算法，理论保证，虽然数据分布不是全局对数凹的。我们证明了几个具有挑战性的多尺度过程是有条件的对数凹小波包正交投影。数值结果显示物理领域，如$\varphi ^4 $$模型和弱透镜收敛映射具有更高的分辨率比以前的作品。
There is a growing gap between the impressive results of deep image generative models and classical algorithms that offer theoretical guarantees. The former suffer from mode collapse or memorization issues, limiting their application to scientific data. The latter require restrictive assumptions such as log-concavity to escape the curse of dimensionality. We partially bridge this gap by introducing conditionally strongly log-concave (CSLC) models, which factorize the data distribution into a product of conditional probability distributions that are strongly log-concave. This factorization is obtained with orthogonal projectors adapted to the data distribution. It leads to efficient parameter estimation and sampling algorithms, with theoretical guarantees, although the data distribution is not globally log-concave. We show that several challenging multiscale processes are conditionally log-concave using wavelet packet orthogonal projectors. Numerical results are shown for physical fields such as the $\varphi^4$ model and weak lensing convergence maps with higher resolution than in previous works.