Renamed loss functions to metrics and added R2 score and Tweedie devi…

…ance

Metrics/README.md

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+# Metrics
+
+## Classification
+
+### Binary cross entropy
+
+<p align="center"><img src="tex/4d11c68926ab6b030d5eddb9e04c79d2.svg?invert_in_darkmode" align=middle width=565.88156955pt height=49.2398742pt/></p>
+
+### Accuracy Score
+
+<p align="center"><img src="tex/db850e0baa86d7832b5c75d7c4488d78.svg?invert_in_darkmode" align=middle width=320.50695269999994pt height=49.2398742pt/></p>
+
+### Hinge Loss
+
+<p align="center"><img src="tex/a2f8c376f4edcf8033377b40424b287d.svg?invert_in_darkmode" align=middle width=265.89446730000003pt height=17.031940199999998pt/></p>
+
+## Regression
+
+### Mean Squared Error
+
+<p align="center"><img src="tex/735371fbbd0b21c453edc23b25d47a60.svg?invert_in_darkmode" align=middle width=292.4476896pt height=49.2398742pt/></p>
+
+### Mean Squared Logarithmic Error
+
+<p align="center"><img src="tex/61e1a35fbe056f586e6a9dbc645eabb7.svg?invert_in_darkmode" align=middle width=441.49680795pt height=49.2398742pt/></p>
+
+### Mean Absolute Error
+
+<p align="center"><img src="tex/5cd6e6c44dcdc5d9134e7ff6c5b812fc.svg?invert_in_darkmode" align=middle width=290.09589345pt height=49.2398742pt/></p>
+
+### Mean Absolute Percentage Error
+
+<p align="center"><img src="tex/d8bc4fe1fed0596068b06f14dc5b6186.svg?invert_in_darkmode" align=middle width=321.60739545pt height=49.2398742pt/></p>
+
+### Median Absolute Error
+
+<p align="center"><img src="tex/ce9e403e07bb796a5a4aea8e9aea8727.svg?invert_in_darkmode" align=middle width=361.860477pt height=16.438356pt/></p>
+
+### Cosine Similarity
+
+<p align="center"><img src="tex/0df67ef21a0ddee56433ca033cb933c1.svg?invert_in_darkmode" align=middle width=506.11591634999996pt height=91.2537549pt/></p>
+
+### R2 Score
+
+<p align="center"><img src="tex/a1b798ffc158c4ee0b440f4114c4f1c0.svg?invert_in_darkmode" align=middle width=216.35715585pt height=41.065845149999994pt/></p>
+
+where <img src="tex/d5d6a7178f9ca2be9eab3bf855709944.svg?invert_in_darkmode" align=middle width=100.29605354999998pt height=27.77565449999998pt/>
+
+## Tweedie deviance
+
+<p align="center"><img src="tex/bfcf5229cb3b2eb7b6472152c5538e88.svg?invert_in_darkmode" align=middle width=604.5553041pt height=100.10823074999999pt/></p>
+
+### Huber Loss
+
+<p align="center"><img src="tex/9152eaad31adde13360d6613b5dcc757.svg?invert_in_darkmode" align=middle width=265.48753109999996pt height=49.315569599999996pt/></p>
+
+### Log Cosh Loss
+
+<p align="center"><img src="tex/1ff5c2fb18f358c5a53d9f38bb1538b8.svg?invert_in_darkmode" align=middle width=300.97297725pt height=49.2398742pt/></p>
+
+## KL Divergence
+
+<p align="center"><img src="tex/2d53cab7cfb446342d0f16408338cde0.svg?invert_in_darkmode" align=middle width=240.76881674999996pt height=49.2398742pt/></p>

Metrics/README.tex.md

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+# Metrics
+
+## Classification
+
+### Binary cross entropy
+
+$$\text{BinaryCrossentropy}(y, \hat{y}) = \frac{1}{n_\text{samples}} \sum_{i=0}^{n_\text{samples} - 1} y_i * \log{\hat{y}_i} + \left(1-y_i\right) * \log{(1-\hat{y}_i)}$$
+
+### Accuracy Score
+
+$$\text{accuracy}(y, \hat{y}) = \frac{1}{n_\text{samples}} \sum_{i=0}^{n_\text{samples}-1} 1(\hat{y}_i = y_i)$$
+
+### Hinge Loss
+
+$$L_\text{Hinge}(y_w, y_t) = \max\left\{1 + y_t - y_w, 0\right\}$$
+
+## Regression
+
+### Mean Squared Error
+
+$$\text{MSE}(y, \hat{y}) = \frac{1}{n_\text{samples}} \sum_{i=0}^{n_\text{samples} - 1} (y_i - \hat{y}_i)^2.$$
+
+### Mean Squared Logarithmic Error
+
+$$\text{MSLE}(y, \hat{y}) = \frac{1}{n_\text{samples}} \sum_{i=0}^{n_\text{samples} - 1} (\log_e (1 + y_i) - \log_e (1 + \hat{y}_i) )^2.$$
+
+### Mean Absolute Error
+
+$$\text{MAE}(y, \hat{y}) = \frac{1}{n_{\text{samples}}} \sum_{i=0}^{n_{\text{samples}}-1} \left| y_i - \hat{y}_i \right|.$$
+
+### Mean Absolute Percentage Error
+
+$$\text{MAPE}(y, \hat{y}) = \frac{1}{n_{\text{samples}}} \sum_{i=0}^{n_{\text{samples}}-1} \frac{{}\left| y_i - \hat{y}_i \right|}{max(\epsilon, \left| y_i \right|)}$$
+
+### Median Absolute Error
+
+$$\text{MedAE}(y, \hat{y}) = \text{median}(\mid y_1 - \hat{y}_1 \mid, \ldots, \mid y_n - \hat{y}_n \mid).$$
+
+### Cosine Similarity
+
+$$\text{cosine similarity}=S_{C}(A,B):=\cos(\theta )={\mathbf {A} \cdot \mathbf {B}  \over \|\mathbf {A} \|\|\mathbf {B} \|}={\frac {\sum \limits _{i=1}^{n}{A_{i}B_{i}}}{{\sqrt {\sum \limits _{i=1}^{n}{A_{i}^{2}}}}{\sqrt {\sum \limits _{i=1}^{n}{B_{i}^{2}}}}}}$$
+
+### R2 Score
+
+$$R^2(y, \hat{y}) = 1 - \frac{\sum_{i=1}^{n} (y_i - \hat{y}_i)^2}{\sum_{i=1}^{n} (y_i - \bar{y})^2}$$
+
+where $\bar{y} = \frac{1}{n} \sum_{i=1}^{n} y_i$
+
+## Tweedie deviance
+
+$$\begin{align} \begin{split}\text{D}(y, \hat{y}) = \frac{1}{n_\text{samples}} \sum_{i=0}^{n_\text{samples} - 1} \begin{cases} (y_i-\hat{y}_i)^2, & \text{for }p=0\text{ (Normal)}\\ 2(y_i \log(y/\hat{y}_i) + \hat{y}_i - y_i),  & \text{for }p=1\text{ (Poisson)}\\ 2(\log(\hat{y}_i/y_i) + y_i/\hat{y}_i - 1),  & \text{for }p=2\text{ (Gamma)}\\ 2\left(\frac{\max(y_i,0)^{2-p}}{(1-p)(2-p)}-\frac{y\,\hat{y}^{1-p}_i}{1-p}+\frac{\hat{y}^{2-p}_i}{2-p}\right), & \text{otherwise} \end{cases}\end{split} \end{align}$$
+
+### Huber Loss
+
+$$L_{\delta }(y, \hat{y})={\begin{cases}{\frac {1}{2}}{(y - )^{2}}&{\text{for }}|a|\leq \delta ,\\\delta (|a|-{\frac {1}{2}}\delta ),&{\text{otherwise.}}\end{cases}}$$
+
+### Log Cosh Loss
+
+$$\text{log cosh} = \frac{1}{n_{\text{samples}}} \sum_{i=0}^{n_{\text{samples}}-1} \log{\left(\cosh{(x)}\right)} $$
+
+## KL Divergence
+
+$$D_{\text{KL}}(y\parallel \hat{y})=\sum_{i=0}^{n_{\text{samples}}-1}y \log{ \left({\frac{y}{\hat{y}}}\right)}$$

Metrics/code/accuracy_score.py

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+import numpy as np
+
+
+class Accuracy:
+    def __call__(self, y: np.ndarray, y_pred: np.ndarray) -> np.float64:
+        return self.loss(y, y_pred)
+
+    def loss(self, y: np.ndarray, y_pred: np.ndarray) -> np.float64:
+        return np.sum(y == y_pred) / y.shape[0]

Metrics/code/median_absolute_error.py

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+import numpy as np
+
+
+class MedianAbsoluteError:
+    def __call__(self, y: np.ndarray, y_pred: np.ndarray) -> np.float64:
+        return self.loss(y, y_pred)
+
+    def loss(self, y: np.ndarray, y_pred: np.ndarray) -> np.float64:
+        return np.median(np.absolute(y - y_pred))

Loss_Functions/poisson_loss/code/poisson.py → Metrics/code/poisson.py

@@ -1,3 +1,4 @@
+# based on https://keras.io/api/losses/probabilistic_losses/#poisson-class
 import numpy as np
 
 

Metrics/code/r2_score.py

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+import numpy as np
+
+
+class R2Score:
+    def __call__(self, y: np.ndarray, y_pred: np.ndarray) -> np.float64:
+        return self.loss(y, y_pred)
+
+    def loss(self, y: np.ndarray, y_pred: np.ndarray) -> np.float64:
+        return 1 - (np.sum(np.power(y-y_pred, 2))) / (np.sum(np.power(y-np.mean(y), 2)))

Metrics/code/tweedie_deviance.py

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+import numpy as np
+
+
+class TweedieDeviance:
+    def __init__(self, power: int) -> None:
+        self.power = power
+
+    def __call__(self, y: np.ndarray, y_pred: np.ndarray) -> np.float64:
+        return self.loss(y, y_pred)
+
+    def loss(self, y: np.ndarray, y_pred: np.ndarray) -> np.float64:
+        if self.power == 0:
+            return np.sum(np.power(y - y_pred, 2)) / y.shape[0]
+        elif self.power == 1:
+            return np.sum(2 * (y * np.log(y / y_pred) + y_pred - y)) / y.shape[0]
+        elif self.power == 2:
+            return np.sum(2 * (np.log(y_pred / y) + y / y_pred - 1)) / y.shape[0]
+        else:
+            return np.sum(2 * (np.power(np.maximum(y, 0), 2-self.power) / ((1-self.power) * (2-self.power)) - (y * np.power(y_pred, 1 - self.power)) / (1 - self.power) + np.power(y_pred, 2 - self.power) / (2 - self.power))) / y.shape[0]