Generalist Forecasting Framework

• Generalist Forecasting Framework is a unified approach that predicts complete seasonal profiles using metadata-driven regression and matrix factorization to reveal shared seasonal patterns.
• It efficiently addresses cold start and warm start challenges by leveraging high-dimensional metadata and partial observations to generate forecasts when historical data is scarce.
• Forecasting entire cycles in one step eliminates cumulative error, enhancing long-range prediction accuracy as demonstrated in large-scale empirical evaluations.

A generalist forecasting framework is a methodological paradigm designed to provide accurate, robust predictions across a diverse array of time series forecasting scenarios, including long-range, cold start, and warm start problems. Such a framework eschews task-specific tailoring in favor of unified principles that leverage both shared statistical structures and external metadata or side information. The approach aims to transcend the limitations of traditional short-term, step-ahead forecasting models, especially in settings characterized by scarce or absent time series history.

1. Unified Modeling Approach

A central innovation lies in reformulating the time series forecasting task as the prediction of entire seasonal profiles. Rather than iteratively projecting one step ahead, the framework organizes all available data so that each seasonal cycle (e.g., a year) corresponds to a column in a shared data matrix. This restructuring amplifies low-dimensional seasonal structure, which is often present across different series and years.

The generative model underpinning the framework is

$$Y_{(i)} = f(\phi_{(i)}) + L R_{(i)} + b + \epsilon_{(i)}$$

where $Y_{(i)}$ is the seasonal profile for the $i$th time series, $\phi_{(i)}$ is a high-dimensional metadata vector, $f(\cdot)$ denotes a regression function, $L$ and $R$ capture shared latent factors, $b$ is an intercept, and $\epsilon_{(i)}$ is Gaussian noise.

The model combines two key components:

• A regression term, $f(\phi_{(i)})$, which predicts the profile using metadata;
• A matrix factorization (MF) term, $L R_{(i)}$, which models shared residual structure after regression. This unified architecture handles long-range, cold start, and warm start forecasting within the same system by leveraging both observed series and auxiliary information.

2. Cold Start and Warm Start Forecasting

The framework specifically addresses situations where little or no historical data is available for certain series:

• Cold Start: When a time series is entirely unobserved, the system relies exclusively on the regression component $f(\phi)$, mapping high-dimensional metadata (such as TF-IDF representations of text descriptions) directly to the expected seasonal profile. This predictive imputation is critical, as standard time series models cannot operate in the absence of past data.
• Warm Start: For series where only an initial (possibly partial) segment of the current cycle is observed, the framework uses the observed partial data to estimate the relevant component of the factor $R$. The combination of $f(\phi)$ and the MF adjustment $L R$ refines the baseline forecast, incorporating both side information and partial temporal signals.

This structure allows the unified framework to function reliably across the spectrum from zero to partial to full historical information—a capability beyond most classical approaches.

3. Long-Range Forecasting without Error Accumulation

Traditional time series approaches often produce long-horizon forecasts by chaining together many single-step predictions, a process vulnerable to cumulative error, especially if the underlying model is misspecified. By contrast, the generalist framework forecasts the entire future seasonal profile in one step, guided by both metadata and learned low-dimensional seasonal patterns. This design bypasses recursive error accumulation and is especially effective in capturing high-level regularities or anomalies manifesting over an entire season.

The reorganization of the data matrix into aligned seasonal profiles ensures that the core low-rank structures become more prominent and easier to exploit, further improving the accuracy and robustness of long-range predictions.

4. Data Matrix Construction and Representation Learning

Data matrix construction is fundamental to the framework's success. Each time series is segmented into fixed-length periods (e.g., years), and these segments are stacked as columns of a joint matrix:

$$Y = [Y_1^1,\, Y_1^{n_1},\, \dotsc,\, Y_N^1,\, \dotsc,\, Y_N^{n_N}]$$

where $T$ is the period length and $N$ the total number of periods (across all series). Corresponding metadata are replicated as needed for each column. This approach amplifies shared structure and enables efficient low-rank matrix modeling, even in the presence of irregularly observed or missing data.

5. Regression and Matrix Factorization Methodologies

Multiple instantiations of the regression component $f(\cdot)$ are supported:

• Low-Rank Linear Regression: Models the profile as $f(\phi) = H U \phi$, where $H \in \mathbb{R}^{T \times k}$ and $U \in \mathbb{R}^{k \times m}$, with $H$ providing the time-variant regression weights and $U$ serving as a projection from high- to lower-dimensional metadata spaces.
• Functional Regression: Employs smooth temporal basis expansions (e.g., B-splines), $f(\phi) = B Q \phi$, enforcing smoothness in predictions across the seasonal cycle.
• Neural Network Regression: Allows the mapping from metadata to the seasonal profile to be nonlinear and data-adaptive.

Following regression, the matrix factorization component approximates residuals as $L R$, capturing additional variability via a low-dimensional latent space. This dual structure allows the framework to model both the explicit, metadata-driven mean profile and the shared, unexplained variations present across different series and periods.

6. Practical Utility and Empirical Evaluation

The framework was empirically validated on major, large-scale datasets, including Google Flu Trends and Wikipedia page traffic. The evaluation assessed performance in four distinct challenges:

• Long-range forecasting;
• Cold start;
• Warm start;
• Missing data imputation.

Error metrics such as average per series thresholded MSE (APST_MSE) and thresholded MAE were used to mitigate the impact of extreme outliers. The unified framework demonstrated superior performance to traditional autoregressive, nearest-neighbor, and alternative matrix factorization baselines (such as TRMF), particularly in cold start and warm start scenarios. Its robustness was observed even in settings with volatile or non-smooth seasonal dynamics, confirming the generalist value of the architecture.

7. Role of Metadata and Limitations

The framework's ability to impute and forecast unobserved or partially observed series is fundamentally reliant on the presence of informative metadata. Side information—such as text-based descriptors, product categories, or regional attributes—must be available and sufficiently discriminative to capture relevant inter-series variation. In the absence of such metadata, the cold start and warm start scenarios become intractable within this framework.

Limitations also exist in the explicit requirement that seasonal repetition be the dominant structure in the data; for non-seasonal or highly non-stationary time series, the advantages of matrix reorganization may become attenuated. However, within domains—such as health surveillance, web traffic, or retail sales—where repeated seasonality and rich metadata are commonplace, the unified generalist framework offers a systematic approach to forecasting that is competitive across a wide range of operational settings.