Kernel Mean Estimation via Spectral Filtering
Authors: Krikamol Muandet, Bharath Sriperumbudur, Bernhard Schölkopf
NeurIPS 2014 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | The paper includes a dedicated section '5 Empirical studies' which describes experiments on synthetic and real data, presenting results in figures and tables, and discussing performance metrics like risk and negative log-likelihood, thus indicating experimental research. |
| Researcher Affiliation | Academia | Krikamol Muandet MPI-IS, T ubingen krikamol@tue.mpg.de Bharath Sriperumbudur Dept. of Statistics, PSU bks18@psu.edu Bernhard Sch olkopf MPI-IS, T ubingen bs@tue.mpg.de |
| Pseudocode | Yes | Table 1: Update equations for β and corresponding filter functions. |
| Open Source Code | No | The paper does not provide an explicit statement or link for open-source code for the described methodology. |
| Open Datasets | Yes | The datasets were taken from the UCI repository1 and pre-processed by standardizing each feature. 1http://archive.ics.uci.edu/ml/ |
| Dataset Splits | Yes | For these two algorithms, we evaluate the leave-one-out score and select βt at the iteration t that minimizes this score (see, e.g., Figure 3(a)). |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., exact GPU/CPU models, processor types with speeds, memory amounts, or detailed computer specifications) used for running its experiments. |
| Software Dependencies | No | The paper does not provide specific ancillary software details with version numbers. |
| Experiment Setup | Yes | To allow for an analytic calculation of the loss L(β, X, P), we assume that the distribution P is a d-dimensional mixture of Gaussians [1, 8]. Specifically, the data are generated as follows: x P4 i=1 πi N(θi, Σi)+ε, θij U( 10, 10), Σi W(3 Id, 7), ε N(0, 0.2 Id) where U(a, b) and W(Σ0, df) are the uniform distribution and Wishart distribution, respectively. As in [1], we set π = [0.05, 0.3, 0.4, 0.25]. Throughout, we use the Gaussian RBF kernel k(x, x ) = exp( x x 2/2σ2) whose bandwidth parameter is calculated using the median heuristic, i.e., σ2 = median{ xi xj 2}. The parameters (πj, θj, σ2 j ) are initialized by the best one obtained from the K-means algorithm with 50 initializations. Throughout, we set r = 5 and use 25% of each dataset as a test set. |