presentation for htbd seminar April

glucose_ts/models/lstm.py

@@ -11,6 +11,8 @@ class VariableLSTM(tf.keras.Model):
             units,
             label_length,
             total_length,
+            norm_std=1.,
+            norm_mean=0.,
             lstm_regularization=0.,
             dense_regularization=0.,
             lstm_dropout=0.,
@@ -21,6 +23,8 @@ class VariableLSTM(tf.keras.Model):
         self.units = units
         self.label_length = label_length
         self.total_length = total_length
+        self.norm_std = tf.convert_to_tensor(norm_std)
+        self.norm_mean = tf.convert_to_tensor(norm_mean)
 
         self.lstm_cell = tf.keras.layers.LSTMCell(
             units,
@@ -137,3 +141,20 @@ class VariableLSTM(tf.keras.Model):
 
         predictions = predictions_array.stack()
         return tf.transpose(predictions, [1, 0, 2])
+
+    # def test_step(self, data):
+    #     # Unpack the data
+    #     x, y = data
+    #     # Compute predictions
+    #     y_pred = self(x, training=False)
+    #
+    #     # redo normalization
+    #     original_y = y * tf.cast(self.norm_std, dtype=y.dtype) + tf.cast(self.norm_mean, dtype=y.dtype)
+    #     original_y_pred = y_pred * tf.cast(self.norm_std, dtype=y_pred.dtype) + tf.cast(self.norm_mean, dtype=y_pred.dtype)
+    #     # Updates the metrics tracking the loss
+    #     self.compiled_loss(original_y, original_y_pred, regularization_losses=self.losses)
+    #     # Update the metrics.
+    #     self.compiled_metrics.update_state(original_y, original_y_pred)
+    #     # Return a dict mapping metric names to current value.
+    #     # Note that it will include the loss (tracked in self.metrics).
+    #     return {m.name: m.result() for m in self.metrics}

notebooks/regression.ipynb

@@ -219,7 +219,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 50,
+   "execution_count": 58,
    "metadata": {},
    "outputs": [
     {
@@ -228,13 +228,14 @@
        "0.2134445901945714"
       ]
      },
-     "execution_count": 50,
+     "execution_count": 58,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "from sklearn.metrics import mean_squared_error\n",
+    "import math\n",
     "\n",
     "mean_squared_error(\n",
     "    lr_model.predict(calibration_df['voltage (V)'].values.reshape(-1, 1)),\n",

presentations/htbd_presentation.tex

@@ -7,6 +7,7 @@
 
 \usepackage[english]{babel}  % 'babel' is necesary to automatically translate certain elements 
 \usepackage[utf8]{inputenc}
+\usepackage{mathtools}
 
 % insert an slide with the section head at the beginning of each section
 \AtBeginSection[]{
@@ -29,7 +30,7 @@
 % parameters
 \title{TF3 Improving signal quality}
 \subtitle{Getting glucose concentrations closer to online}
-\author[Christoph Lange]{Christoph Lange, Katharina Paulick, Bo Kern}
+\author[Christoph Lange]{Bo Kern, Christoph Lange, Katharina Paulick, Meijiao Wan, Niko Dejonge}
 \institute{Technische Universität Berlin}
 
 % footer logo
@@ -91,19 +92,41 @@
 
 \begin{frame}{Microscopic Image Analysis}
 \smallHead
-We aim for:
+
+\begin{columns}
+\column{0.47 \textwidth}	
+	We aim for:
+	\begin{itemize}
+		\item analyzing cell cultures offline
+		\item staining the membranes
+		\item automatically cut one picture into multiple
+		\item retrieve parameters that describe the cell morphology
+		\item train a model that predicts the at-line quantities
+	\end{itemize}
+
+	\begin{figure}[h!]
+	\includegraphics[scale=0.1]{images/cell_parameter.png}
+	\end{figure}
+
+
+\column{0.5 \textwidth}	
+
+	\begin{figure}[h!]
+	\includegraphics[scale=0.16]{images/old_new_image.png}
+	\end{figure}
+\end{columns}
+\end{frame}
+
+
+\begin{frame}{Vision: Sensor Fusion}
+\smallHead
+We want to
 \begin{itemize}
-	\item analyzing cell cultures offline
-	\item staining the membranes
-	\item automatically cut one picture into multiple
-	\item retrieve parameters that describe the cell morphology
-	\item train a model that predicts the at-line quantities
+	\item combine different sensor source to predict at-line parameters
+	\item Integrate signal processing algorithms into a model evaluation framework with the supervised models from TF1
+	\item Comparison of different signal processing mechanisms on the respective sensor signal
 \end{itemize}
 
-\begin{figure}[h!]
-\includegraphics[scale=0.2]{images/microscopic_images.png}
-
-\end{figure}
 
 \end{frame}
 
@@ -124,7 +147,7 @@ We aim for:
 		\item one measurement at a time
 		\item enzyme based amperometric sensors
 		\item enables at-line measurements
-		\item integrated via SILA
+		\item integrated via SiLA
 	\end{itemize}
 
 \column{0.5 \textwidth}
@@ -163,8 +186,40 @@ We aim for:
 
 
 
+\subsection{Time Series Forecasting}
+
+
+\begin{frame}{Time Series Dataset}
+\smallHead
+
+\begin{columns}
+
+\column{0.4 \textwidth}
+
+The dataset consists of $43$ time series from different sensors and runs
+
+\begin{itemize}
+	\item $1000$ voltage measurements $V_i$
+	\item equidistant points in time $t_i$ for $9$ minutes
+	\item mostly starting at $1.02 V$
+	\item mostly decreasing
+	\item different noise levels
+\end{itemize}
+
+\emph{Goal:} Get the final value earlier
+
+
+\column{0.55 \textwidth}
+	\begin{figure}[h!]
+	\includegraphics[width=\linewidth, height=5.2cm]{images/time_series_dataset.png}
+
+	\end{figure}
+\end{columns}
+
+\end{frame}
+
 
-\begin{frame}{Time Series}
+\begin{frame}{Time Series as Generalized Logistic Curve}
 \smallHead
 
 \begin{columns}
@@ -194,7 +249,7 @@ We observe a fit for the whole time horizon.
 \end{frame}
 
 
-\begin{frame}{Predicting Time Series}
+\begin{frame}{Predicting Time Series: Maximum Likelihood}
 \smallHead
 
 \begin{columns}
@@ -220,6 +275,118 @@ model overfits to first part
 	\end{figure}
 \end{columns}
 
+\end{frame}
+
+\begin{frame}{Predicting Time Series: Maximum a Posteriori}
+\smallHead
+
+\begin{columns}
+
+\column{0.4 \textwidth}
+
+\begin{itemize}
+	\item cut time series after $t_c = 2$ minutes
+	\item we have time, voltage pairs $ V_i, t_i $
+	\item try to estimate A, K, B, M and $\nu$ 
+	\item use maximum a posteriori
+	\item gaussian priors for A, K, B, M and $\nu$ 
+	\item assumption that all parameter are independent
+\end{itemize}
+
+model looks fine for this one sample.
+
+\column{0.5 \textwidth}
+	\begin{figure}[h!]
+	\includegraphics[width=\linewidth, height=5.2cm]{images/cut_off_map.png}
+
+	\end{figure}
+\end{columns}
+
+\end{frame}
+
+
+\begin{frame}{Predicting Time Series: LSTM}
+\smallHead
+
+\begin{columns}
+
+\column{0.4 \textwidth}
+
+\begin{itemize}
+	\item reduce number of data points by factor $20$
+	\item cut time series after $t_c = 1.8 $ minutes
+	\item model just cares about the voltages $\{ V_i  | t_i  \leq t_c \} $
+	\item predict one step at a time  
+	\item feed the last prediction as input for the next one
+\end{itemize}
+
+Shorter input horizons, fit looks acceptable
+
+\column{0.5 \textwidth}
+	\begin{figure}[h!]
+	\includegraphics[scale=0.16]{images/lstm_examples.png}
+
+	\end{figure}
+\end{columns}
+
+\end{frame}
+
+
+\begin{frame}{Evaluating the LSTM}
+\smallHead
+
+\begin{columns}
+
+\column{0.4 \textwidth}
+
+Define a "final" voltage as the mean after $t_f = 7 $.
+\begin{equation*}
+V_f \coloneqq \frac 1 {\left| \{i \in \mathbb{N} |  t_i \geq t_f  \} \right|}  \sum_{ i \in \{i \in \mathbb{N} |  t_i \geq t_f  \}}  V_i
+\end{equation*}
+
+and take a look at the distribution of the residuals
+
+\begin{equation*}
+ \hat{V_f} - V_f 
+\end{equation*}
+
+and the mean squared error for $N$ time series amounts to 
+
+\begin{equation*}
+\frac 1 N \sum (\hat{V_f} - V_f )^2  \approx 10^{-4}
+\end{equation*}
+
+
+
+\column{0.5 \textwidth}
+	\begin{figure}[h!]
+	\includegraphics[scale=0.27]{images/residuals.png}
+
+	\end{figure}
+\end{columns}
+
+\end{frame}
+
+
+\subsection{Open Questions}
+
+
+\begin{frame}{Open Questions}
+\smallHead
+
+\begin{itemize}
+	\item Can we get the voltage curves more consistent?
+	\item Is a straight line the right model family for the regression problem glucose / voltage regression problem?
+	\item Two separate models vs. a joint model predicting glucose directly?
+	\item Can we use a physics informed neural network?
+	\item What is the performance of the Generalized Logistic Curve model?
+	\item Can we predict sooner?
+	\item Do the curves change when we have a real batch fermentation?
+	\item More parallel measurements?
+\end{itemize}
+
+
+
 \end{frame}
 
 
@@ -239,8 +406,8 @@ model overfits to first part
 		\item \href{http://git-workshop-py-packaging.rtfd.io/}{Python Packaging}
 	\end{itemize}
 	\item \href{https://git.tu-berlin.de/bvt-htbd/kiwi/cookiecutter-python-package-template}{Python Package Template} and \href{https://kiwi-python-package-template.readthedocs.io/en/latest/index.html}{documentation} how to use it
-	\item Continuous Integration
-	\item Sphinx documentation
+	\item Continuous Integration for HTBD
+	\item \href{https://glucose-ts.readthedocs.io/en/latest/}{Sphinx documentation} for the Glucose Models to ease the usage
 \end{itemize}
 
 \column{0.5 \textwidth}
@@ -253,5 +420,12 @@ model overfits to first part
 \end{frame}
 
 
+\begin{frame}{}
+  \centering \Huge
+  \emph{Questions ?}
+\end{frame}
+
+
+
 
 \end{document}