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\title[Robust Forecasting]{Robust Probabilistic Forecasting at Scale}
\subtitle{Methods, Benchmarks, and Deployment Lessons}
\author[F.\ Last]{First Last}
\institute[Example U]{School of Statistics \\ University of Example}
\date{\today}

\begin{document}

\frame{\titlepage}

\begin{frame}{Outline}\tableofcontents\end{frame}

\section{Introduction}
\subsection{Background}
\begin{frame}{Background}
Probabilistic forecasting estimates a full predictive distribution over future values,
not a single point estimate. This is essential in finance, energy, and logistics.
\end{frame}

\subsection{Motivation}
\begin{frame}{Motivation}
  \begin{itemize}
    \item Point forecasts under-represent risk.
    \item Decision-making requires quantiles and coverage.
    \item Existing methods scale poorly to millions of series.
  \end{itemize}
\end{frame}

\section{Method}
\subsection{Overview}
\begin{frame}{Method Overview}
We combine an autoregressive encoder with a quantile regression head. The model
shares parameters across all series via learned embeddings.
\end{frame}

\subsection{Details}
\begin{frame}{Loss Function}
We train with the pinball loss at $Q$ quantile levels:
\[
  \mathcal{L}(\hat{y}, y) = \sum_{q\in Q}\max\big( q(y - \hat y_q),\; (q-1)(y - \hat y_q) \big).
\]
This yields calibrated quantile estimates without distributional assumptions.
\end{frame}

\begin{frame}{Architecture}
\begin{itemize}
  \item Temporal encoder: dilated convolutions for $O(\log T)$ receptive field.
  \item Series embedding: 32-dim learned per-series vector.
  \item Quantile head: shared MLP producing 9 quantiles in one pass.
\end{itemize}
\end{frame}

\section{Results}
\begin{frame}{Benchmarks}
\begin{table}
\centering
\begin{tabular}{lccc}
\toprule
Method & CRPS $\downarrow$ & MAPE $\downarrow$ & Train (h) $\downarrow$ \\
\midrule
ARIMA         & 0.82 & 12.4 &  3 \\
DeepAR        & 0.64 &  9.1 & 18 \\
TFT           & 0.58 &  8.3 & 26 \\
\textbf{Ours} & \textbf{0.49} & \textbf{7.2} & \textbf{11} \\
\bottomrule
\end{tabular}
\end{table}
\end{frame}

\begin{frame}{Coverage}
At the nominal 90\% level, our intervals achieve 89.6\% empirical coverage across
three hold-out datasets --- a marked improvement over miscalibrated baselines.
\end{frame}

\section{Conclusion}
\begin{frame}{Summary}
  \begin{itemize}
    \item Strong accuracy-efficiency trade-off.
    \item Calibrated quantiles without distributional assumptions.
    \item Deployed at \textgreater 1M series in production.
  \end{itemize}
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\begin{frame}{Thank You}
\centering
\Huge Questions?\\[0.8em]
\normalsize [email protected]
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