Inexact Tensor Methods with Dynamic Accuracies
Authors: Nikita Doikov, Yurii Nesterov
ICML 2020 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Lastly, we present computational results on a variety of machine learning problems for several methods and different accuracy policies. and Let us demonstrate computational results with empirical study of different accuracy policies. We consider inexact methods of order p = 2 (Cubic regularization of Newton method), and to solve the corresponding subproblem we call the Fast Gradient Method with restarts from (Nesterov, 2019b). and 5.1. Logistic Regression First, let us consider the problem of training ℓ2-regularized logistic regression model for classification task with two classes, on several real datasets2: mashrooms (m = 8124, n = 112), w8a (m = 49749, n = 300), and a8a (m = 22696, n = 123)3. |
| Researcher Affiliation | Academia | 1Institute of Information and Communication Technologies, Electronics and Applied Mathematics (ICTEAM), Catholic University of Louvain (UCL), Belgium 2Center for Operations Research and Econometrics (CORE), Catholic University of Louvain (UCL), Belgium. |
| Pseudocode | Yes | Algorithm 1 Monotone Inexact Tensor Method, I and Algorithm 2 Monotone Inexact Tensor Method, II and Algorithm 3 Inexact Tensor Method with Averaging and Algorithm 4 Accelerated Scheme. |
| Open Source Code | Yes | The source code can be found at https://github. com/doikov/dynamic-accuracies/ |
| Open Datasets | Yes | 5.1. Logistic Regression First, let us consider the problem of training ℓ2-regularized logistic regression model for classification task with two classes, on several real datasets2: mashrooms (m = 8124, n = 112), w8a (m = 49749, n = 300), and a8a (m = 22696, n = 123)3. 2https://www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets/ |
| Dataset Splits | No | The paper mentions using 'real datasets' for 'training ℓ2-regularized logistic regression model' but does not specify any dataset split information for training, validation, or testing. |
| Hardware Specification | Yes | Clock time was evaluated using the machine with Intel Core i5 CPU, 1.6GHz; 8 GB RAM. |
| Software Dependencies | No | All methods were implemented in Python. The paper mentions Python as the implementation language but does not specify its version or the versions of any other software libraries or dependencies. |
| Experiment Setup | Yes | We use the standard Euclidean norm for this problem, and simple line search at every iteration, to fit the regularization parameter H. and We set m = 6n, and n = 100. In the method, we use the following Euclidean norm for the primal space: x = Bx, x 1/2, with the matrix B = Pm i=1 aia T i , and fix regularization parameter H being equal 1. |