基于LSTM网络的时间序列预测：缺失数据处理方案咨询

Hey there! Let's break down how to handle those annoying inconsistent gaps in your time-series dataset—your initial thought about using a special vector makes sense on the surface, but as you’ve noticed, it can quickly make training data unwieldy. Here’s a breakdown of the best approaches tailored to your setup:

Before jumping into fixes, it’s critical to categorize your missing data—this dictates which methods will work:

• MCAR (Missing Completely at Random): Missingness has nothing to do with the data itself (e.g., a sensor glitch randomly skipped a measurement). Most methods work here.
• MAR (Missing at Random): Missingness relates to observed data (e.g., users with lower value1 are less likely to be measured on busy days). You’ll need methods that account for these correlations.
• MNAR (Missing Not at Random): Missingness relates to unobserved data (e.g., a user skipped a measurement because their value2 was abnormally high). This is trickiest—you may need to model the missingness process itself.

Imputation-Focused Methods #

These fill in missing values while preserving temporal context:

• Forward/Backward Fill (LOCF/NOCF): Super simple for short gaps where measurements are stable. Group by user_id, then fill missing value1/value2 with the last (or next) recorded value. Just avoid this for long gaps—it’ll introduce bias.
• Temporal Interpolation: Linear interpolation works well for small, steady gaps; spline interpolation is better if your values follow non-linear trends. For example, in pandas you’d do something like:

  df.groupby('user_id').apply(lambda x: x.set_index('measurement_date').interpolate(method='linear'))
  

• Model-Based Imputation: Train time-series models to predict missing values. Options include:
  • ARIMA or SARIMA for users with clear seasonal/trend patterns.
  • LSTMs or Transformers for complex, non-linear user-specific trends. You can train a single model with user IDs as features, or separate models for high-data users.

Feature Engineering (No Imputation Needed) #

Instead of filling gaps, turn missingness into useful features:

• Add binary flags like is_missing_value1 to explicitly tell your model when a value is absent.
• Calculate days_since_last_measurement to capture gap length—this often correlates with how much the value might have changed.
• Compute rolling stats per user (e.g., mean_value2_last_14_days, max_value1_last_month) to give the model context even when the current value is missing.

Directly Handle Gaps with Sequence Models #

If you’re using deep learning, skip imputation entirely with models built for variable-length data:

• Use masked layers (available in TensorFlow/PyTorch) to mark missing values. The model will ignore these entries during training instead of learning from arbitrary placeholders.
• Transformer-based models (like Temporal Fusion Transformers) excel at irregular time series—they use attention mechanisms to focus on relevant observed data points, even with big gaps.

You’re right to be skeptical:

• Models can learn spurious patterns from the placeholder (e.g., associating -999 with low value1 when there’s no real link).
• Generating rows for every possible date to insert the placeholder bloats your dataset, wasting compute resources.
• For tree-based models (like Random Forests), while NaNs are handled natively, you still lose the temporal context of how long the gap was.

• Gap Length: Short gaps (1-3 days) → LOCF/interpolation. Long gaps → model-based imputation or feature engineering.
• Per-User Data: If users have hundreds of measurements → per-user models. If users are sparse → global models with user features.
• End Goal: Predicting future values → masked sequence models or model-based imputation. User segmentation → feature engineering with missing flags.

内容的提问来源于stack exchange，提问作者Alice