Furthermore, our S et-based N eural network E ncoder (SNE) takes into consideration the hierarchical computational structure of neural networks.

Neural Information Processing Systems http://nips.cc/

We focus on the setting where firms are not aware of demand functions and how reference prices areformed but haveaccess to an oracle that provides a measure of consumers' responsiveness to the current posted prices.

Scikit - learn: Machinelearninginpython.the Journalofmachine Learningresearch, 12: 2825-2830, 2011.

The Information Contrastive (I-Con) framework revealed that over 23 representation learning methods implicitly minimize KL divergence between data and learned distributions that encode similarities between data points. However, a KL-based loss may be misaligned with the true objective, and properties of KL divergence such as asymmetry and unboundedness may create optimization challenges. We present Beyond I-Con, a framework that enables systematic discovery of novel loss functions by exploring alternative statistical divergences. Key findings: (1) on unsupervised clustering of DINO-ViT embeddings, we achieve state-of-the-art results by modifying the PMI algorithm to use total variation (TV) distance; (2) supervised contrastive learning with Euclidean distance as the feature space metric is improved by replacing the standard loss function with Jenson-Shannon divergence (JSD); (3) on dimensionality reduction, we achieve superior qualitative results and better performance on downstream tasks than SNE by replacing KL with a bounded $f$-divergence. Our results highlight the importance of considering divergence choices in representation learning optimization.

Understanding and identifying controlled direct effects (CDEs) is crucial across numerous scientific domains, including public health. While existing methods can identify these effects from causal directed acyclic graphs (DAGs), the true underlying structure is often unknown in practice. Essential graphs, which represent a Markov equivalence class of DAGs characterized by the same set of $d$-separations, provide a more practical and realistic alternative. However, learning the full essential graph is computationally intensive and typically depends on strong, untestable assumptions. In this work, we characterize a local class of graphs, defined relative to a target variable, that share a specific subset of $d$-separations, and introduce a graphical representation of this class, called the local essential graph (LEG). We then present LocPC, a novel algorithm designed to recover the LEG from an observed distribution using only local conditional independence tests. Building on LocPC, we propose LocPC-CDE, an algorithm that discovers the portion of the LEG that is both sufficient and necessary to identify a CDE, bypassing the need of retrieving the full essential graph. Compared to global methods, our algorithms require less conditional independence tests and operate under weaker assumptions while maintaining theoretical guarantees. We illustrate the effectiveness of our approach through simulation studies.

Furthermore, our S et-based N eural network E ncoder (SNE) takes into consideration the hierarchical computational structure of neural networks.

We consider the dynamic price competition between two firms operating within an opaque marketplace, where each firm lacks information about its competitor. The demand follows the multinomial logit (MNL) choice model, which depends on the consumers'