The Statistical Performance of Collaborative Inference
Authors: Gérard Biau, Kevin Bleakley, Benoît Cadre
JMLR 2016 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In Section 5 we present the remarkable Ramanujan expander graphs and analyze the tradeoff between statistical efficiency and communication complexity for these graphs with a series of simulation studies. Lastly, Section 6 provides several elements for analysis of more complicated asynchronous models with delays. Figure 4 shows results for 3- and 5-regular Ramanujan-type matrices (A3 and A5) as well as the previous results for non-Ramanujan-type matrices A0, A1, and A2 (see Figure 2). Figure 5: Statistical efficiency vs communication complexity tradeoff for four different node communication penalties β. d is the d which minimizes S (Ad) + βC (Ad). Figure 6: Optimizing the number of nodes N and the level of communication d required between nodes to obtain a performance ratio τt(Ad) ≥ 0.99 given a large fixed quantity of data T. |
| Researcher Affiliation | Academia | Gerard Biau EMAIL Laboratoire de Statistique Théorique et Appliquée, FRE CNRS 3684 Université Pierre et Marie Curie Boîte 158, 4 place Jussieu 75005, Paris, France Kevin Bleakley EMAIL INRIA Saclay Ile-de-France 1 rue Honoré d Estienne d Orves 91120, Palaiseau, France Benoît Cadre EMAIL IRMAR, ENS Rennes Campus de Ker Lann Avenue Robert Schuman 35170 Bruz, France |
| Pseudocode | No | The paper describes methods using mathematical equations and prose. No explicitly labeled pseudocode blocks or algorithms (e.g., 'Algorithm 1') are present. |
| Open Source Code | No | The paper does not contain any explicit statements about making source code available, nor does it provide links to repositories or mention code in supplementary materials. |
| Open Datasets | No | In the trials shown, i.i.d. uniform random variables on [0, 1] are delivered online to N = 5 nodes, one to each at each time t. The paper uses simulated data (i.i.d. uniform random variables) rather than a named, publicly available dataset. No specific dataset source, link, or citation is provided. |
| Dataset Splits | No | The paper uses simulated data (i.i.d. uniform random variables). As such, it does not describe or require training/test/validation dataset splits typically found with pre-existing datasets. |
| Hardware Specification | No | The paper conducts "simulation studies" but does not specify any hardware details (e.g., CPU, GPU models, or memory) used for these simulations. |
| Software Dependencies | No | The paper describes theoretical models and simulation studies but does not specify any software dependencies (e.g., programming languages, libraries, or tools with version numbers) used for its implementation or analysis. |
| Experiment Setup | Yes | In the trials shown, i.i.d. uniform random variables on [0, 1] are delivered online to N = 5 nodes, one to each at each time t. [...] Figure 6: Optimizing the number of nodes N and the level of communication d required between nodes to obtain a performance ratio τt(Ad) ≥ 0.99 given a large fixed quantity of data T. The minimum is found at (N, d ) = (710, 3), suggesting that with 100 million data points, one can get excellent performance results (τt(Ad ) ≥ 0.99) for a low cost with around 700 nodes, each connected only to three other nodes! Increasing N further raises the cost necessary to obtain the same performance, both due to the price of adding more nodes, as well as requiring more connections between them: d must increase to 4, 5, and so on. |