add readme

README.md

@@ -34,24 +34,35 @@ At minium, the metric requires the original time-series and the generated time-s
 ### Inputs
 - **predictions**: (list of list of list of float or numpy.ndarray): The generated time-series. The shape of the array should be `(num_generation, seq_len, num_features)`.
 - **references**: (list of list of list of float or numpy.ndarray): The original time-series. The shape of the array should be `(num_reference, seq_len, num_features)`.
+- **batch_size**: (int, optional): The batch size for computing the metric. This affects quadratically. Default is None.
 
 ### Output Values
 
-*Explain what this metric outputs and provide an example of what the metric output looks like. Modules should return a dictionary with one or multiple key-value pairs, e.g. {"bleu" : 6.02}*
+Let prediction instances be $P = \{p_1, p_2, \ldots, p_n\}$ and reference instances be $R = \{r_1, r_2, \ldots, r_m\}$.
 
-*State the range of possible values that the metric's output can take, as well as what in that range is considered good. For example: "This metric can take on any value between 0 and 100, inclusive. Higher scores are better."*
+- **matching_mse**: (float): Average of the MSE between the generated instance and the reference instance with the lowest MSE. Intuitively, This is similar to precision in classification. In the equation, $\frac{1}{n} \sum_{i=1}^{n} \min_{j} \mathrm{MSE}(p_i, r_j)$.
+- **covered_mse**: (float): Average of the MSE between the reference instance and the  with the lowest MSE. Intuitively, This is similar to recall in classification. In the equation, $\frac{1}{m} \sum_{j=1}^{m} \min_{i} \mathrm{MSE}(p_i, r_j)$.
+- **harmonic_mean**: (float): Harmonic mean of the matching_mse and covered_mse. This is similar to F1-score in classification.
+- **index_mse**: (float): Average of the MSE between the generated instance and the reference instance with the same index. In the equation, $\frac{1}{n} \sum_{i=1}^{n} \mathrm{MSE}(p_i, r_i)$.
+- **matching_mse_features**: (list of float): matching_mse computed individually for each feature.
+- **covered_mse_features**: (list of float): covered_mse computed individually for each feature.
+- **harmonic_mean_features**: (list of float): harmonic_mean computed individually for each feature.
+- **index_mse_features**: (list of float): index_mse computed individually for each feature.
+- **macro_matching_mse**: (float): Average of the matching_mse_features.
+- **macro_covered_mse**: (float): Average of the covered_mse_features.
+- **macro_harmonic_mean**: (float): Average of the harmonic_mean_features.
 
 #### Values from Popular Papers
-*Give examples, preferrably with links to leaderboards or publications, to papers that have reported this metric, along with the values they have reported.*
+<!-- *Give examples, preferrably with links to leaderboards or publications, to papers that have reported this metric, along with the values they have reported.* -->
 
 ### Examples
-*Give code examples of the metric being used. Try to include examples that clear up any potential ambiguity left from the metric description above. If possible, provide a range of examples that show both typical and atypical results, as well as examples where a variety of input parameters are passed.*
+<!-- *Give code examples of the metric being used. Try to include examples that clear up any potential ambiguity left from the metric description above. If possible, provide a range of examples that show both typical and atypical results, as well as examples where a variety of input parameters are passed.* -->
 
 ## Limitations and Bias
-*Note any known limitations or biases that the metric has, with links and references if possible.*
+This metric is based on the assumption that the generated time-series should match the original time-series. This may not be the case in some scenarios. The metric may not be suitable for evaluating time-series generation models that are not required to match the original time-series.
 
 ## Citation
-*Cite the source where this metric was introduced.*
+<!-- *Cite the source where this metric was introduced.* -->
 
 ## Further References
-*Add any useful further references.*
+<!-- *Add any useful further references.* -->