Kernels for Sequentially Ordered Data
Authors: Franz J. Kiraly, Harald Oberhauser
JMLR 2019 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We perform two experiments to validate the practical usefulness of the signature kernels: (1) On a real world data set of hand movement classification (eponymous UCI data set Sapsanis et al. (2013)), we show the discretized signature kernel outperforms the best previously reported predictive performance Sapsanis et al. (2013), as well as non-sequential kernel and aggregate baselines. (2) On a real world data set on hand written digit recognition (pendigits), we show that the discretized signature kernel over the Euclidean kernel (= linear use of signature features) achieves only sub-baseline performance. Using the discretized signature kernel over a Gaussian kernel improves prediction accuracy to the baseline region. |
| Researcher Affiliation | Academia | Franz J. Kir aly EMAIL Department of Statistical Science University College London London WC1E 6BT, United Kingdom Harald Oberhauser EMAIL Mathematical Institute University of Oxford Oxford OX2 6GG, United Kingdom |
| Pseudocode | Yes | Algorithm 1 Computing the cumulative sum of a vector. Algorithm 2 Computing the cumulative sum of an array. Algorithm 3 Evaluation of k+ m. Algorithm 4 Evaluation of k+ m, with low-rank speed-up. Algorithm 5 Computation of the Gram matrix of k+ m, with (double) low-rank speed-up. Algorithm 6 Evaluation of k+ (d,m). |
| Open Source Code | No | Section 7 presents a Numpy implementation and basic benchmarks. However, the paper does not explicitly state that the code is open-source or provide a link to a repository. |
| Open Datasets | Yes | We performed classification with the eps-support vector machine (SVC) on the hand movements data set from UCI Sapsanis et al. (2013). We performed classification on the pendgits data set from the UCI repository16. It contains 10992 samples of digits between 0 and 9 written by 44 different writers with a digital pen on a tablet. One sample consists of a pair of horizontal and vertical coordinates of sampled at 8 different time points, hence we deal with a sequence in X8 with X = R2. The data set comes with a pre-specified training fold of 7494 samples, and a test fold of 3498 samples. |
| Dataset Splits | Yes | In all experiments, we use nested (double) cross-validation for parameter tuning (inner loop) and estimation of error metrics (outer loop). In both instances of cross-validation, we perform uniform 5-fold cross-validation. The data set comes with a pre-specified training fold of 7494 samples, and a test fold of 3498 samples. |
| Hardware Specification | No | The paper mentions 'contemporary desktop computers' in Section 6.3 but does not provide specific hardware details (e.g., CPU, GPU models, memory, etc.) for running experiments. |
| Software Dependencies | No | For prediction, we use eps-support vector classification (as available in the python/scikitlearn package). Section 7 presents a Numpy implementation and basic benchmarks. The paper mentions 'python/scikit-learn' and 'Numpy' but does not provide specific version numbers for these software components. |
| Experiment Setup | Yes | In all experiments, we use nested (double) cross-validation for parameter tuning (inner loop) and estimation of error metrics (outer loop). In both instances of cross-validation, we perform uniform 5-fold cross-validation. Unless stated otherwise, parameters are tuned on the tuning grid given in Table 3 (when applicable). Kernel parameters are the same as in the above section prediction mehods . The best parameter is selected by 5-fold cross-validation, as the parameter yielding the minimum test-f1-score, averaged over the five folds. |