💻 computer science

Research on Enterprise Cost Prediction Method Based on Improved Informer Model

This paper proposes an improved Informer-based model incorporating a standard deviation-based dynamic denoising algorithm and a volatility-aware adaptive sampling mechanism to enhance the accuracy and stability of enterprise cost predictions, demonstrating superior performance over existing methods on both enterprise and benchmark datasets.

Original authors: Nan Ban, Li Cao, Yiping Yuan, Feng Tan, Jingjing Li

Published 2026-08-10

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Nan Ban, Li Cao, Yiping Yuan, Feng Tan, Jingjing Li

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to predict the weather for next month. You look at the sky, but it's a chaotic mess of sudden storms, weird heat spikes, and random clouds that don't mean anything. If you try to guess the temperature based on that noise, you'll probably get it wrong. This is the daily struggle of "time series forecasting," a branch of science where computers try to predict the future based on a line of past data. Usually, these computers are like super-smart students who are great at spotting patterns, but they get easily distracted by "noise"—sudden, weird jumps in the data that aren't real trends, just glitches or accidents.

To solve this, scientists have built a special tool called the "Informer." Think of the Informer as a super-efficient librarian who can read a million books (data points) in a second without getting a headache. It uses a trick called "sparse attention," which is like the librarian deciding to only read the most important chapters of a book to save time, rather than reading every single word. However, even this super-librarian has a weakness: when the data is messy and jumps around wildly (like enterprise costs), the librarian might accidentally skip the most exciting, important plot twists because they are trying to be too efficient. This paper tackles that specific problem.

The Problem: When the Data Goes Wild

Imagine you are the manager of a giant factory. Every day, you need to know how much money you're going to spend next week, next month, or even next year. This is called "enterprise cost prediction." But cost data is messy. Sometimes, a raw material price suddenly spikes because of a shipping delay, or a machine breaks down unexpectedly. These are "extreme values"—sudden, loud noises in the data that look like big trends but are actually just accidents.

Older computer models get confused by these accidents. They think a one-day spike in spending is a new rule for the future, leading them to make bad predictions. Even the smart "Informer" model, which is usually great at long-term predictions, struggles here. It tries to be efficient by randomly picking which data points to focus on, but in a chaotic cost environment, it might accidentally ignore the very spikes that matter most, or get distracted by the noise.

The Solution: A Smarter, More Attentive Librarian

The authors of this paper, Nan Ban and their team, decided to give the Informer a serious upgrade. They didn't just throw more data at it; they taught it two new skills to handle the chaos of real-world business costs.

Skill 1: The "Noise-Canceling Headphones" (Dynamic Denoising)
First, they added a pre-processing step. Imagine the data is a song full of static and popping sounds. Before the Informer listens to the song, this new algorithm puts on noise-canceling headphones. It looks at the data and asks, "Is this a real trend, or just a glitch?"

If a number is way too high or low compared to its neighbors (like a sudden, impossible jump in office supply costs), the algorithm doesn't just delete it—that would lose important information. Instead, it "smooths" it out, like gently blending a rough edge so it fits the curve better.
Crucially, this isn't a one-size-fits-all filter. The algorithm is smart enough to know that some costs (like raw materials) are naturally wild and jumpy, while others (like office rent) are calm. It adjusts its sensitivity accordingly, keeping the real "wild" trends while scrubbing away the fake noise.

Skill 2: The "Spotlight on the Action" (Volatility-Aware Sampling)
Once the data is cleaner, the Informer has to decide what to read. The original Informer picks data points somewhat randomly to save time. The new version, however, uses a "volatility-aware" strategy.

Think of this like a camera operator at a concert. If the band is playing a slow, boring ballad, the camera stays still. But if the drummer starts a crazy, fast solo (high volatility), the camera zooms in and follows every beat.
The new model does the same thing. It calculates how much a specific chunk of data is shaking or jumping. If a chunk is highly volatile (lots of action), the model forces itself to pay extra attention to it, ensuring it doesn't miss the important spikes. If the data is calm, it takes a breather. This ensures the model captures the "plot twists" in the cost story without getting overwhelmed.

What They Found: Better Predictions for the Middle Term

The team tested their new "Super-Informer" on real data from a tobacco company and a standard electricity dataset. They compared it against the original Informer and other models.

The results showed that their new method is a clear winner, especially for predicting the future a bit further out (the "medium term").

For a 12-step prediction (looking 12 time periods ahead), the new model reduced the error (MSE) to 0.3819 and the average absolute error (MAE) to 0.3449. This was a 2.1% and 2.2% improvement over a model that only did the noise-canceling step.
For a 24-step prediction, the error dropped to 0.5035 (MSE) and 0.4202 (MAE), showing a slight but steady improvement of 0.1% and 0.2% respectively.

Interestingly, the authors noted that for very short-term predictions (6 steps), the new model was slightly less accurate than the denoised-only version. This is because short-term predictions are simple enough that the extra "spotlight" isn't needed yet. But as you look further into the future, where the noise and volatility really matter, the new model shines. It avoids the "false low errors" of models that get tricked by noise, providing a more stable and reliable view of where costs are heading.

Why This Matters

This isn't just a math exercise; it's about helping businesses sleep better at night. By accurately predicting cost trends, companies can spot potential budget overruns early and fix them before they become disasters. The authors suggest that this "denoising plus spotlight" approach creates a perfect team: one part cleans the data, and the other part focuses on the most important, chaotic parts of the story.

While the paper shows these results are solid on the datasets they tested, the authors are already looking ahead. They plan to add even more factors to the mix, like raw material prices and policy changes, to make the predictions even sharper. For now, though, they've proven that when you teach a computer to ignore the noise and focus on the real action, it can tell you a much better story about the future.

Technical Summary: Research on Enterprise Cost Prediction Method Based on Improved Informer Model

Problem Statement
Accurate enterprise cost forecasting is critical for resource allocation and risk control, yet it faces significant challenges due to the high noise and high volatility inherent in cost data. Traditional forecasting models often struggle with gradient vanishing or prediction bias when handling anomalous data, such as sudden raw material price fluctuations or policy adjustments. Furthermore, while the Informer model has demonstrated success in long-sequence time series forecasting (LSTF) for domains like power loads, its direct application to enterprise cost data reveals two key bottlenecks:

Noise Sensitivity: The model's learning of normal cost trends is significantly interfered with by extreme values and outliers, leading to predictions that deviate from reality.
Inflexible Sampling: The standard ProbSparse attention mechanism in the original Informer employs random sampling that ignores the specific fluctuation characteristics of data. This fixed approach fails to adequately capture high-frequency fluctuations in volatile cost scenarios (e.g., equipment maintenance costs) while maintaining efficiency in stable scenarios.

Methodology
The study proposes an improved Informer model that integrates optimized data preprocessing with an enhanced sampling strategy to address the specific characteristics of enterprise cost data. The architecture retains the encoder-decoder structure of the original Informer but introduces two core modifications:

Dynamic Denoising Algorithm (Based on Standard Deviation):
- Objective: To identify and smooth outliers without deleting key trend information (e.g., sudden price shocks).
- Mechanism: The algorithm utilizes a sliding window to calculate local mean ( $\mu_t$ $μ_{t}$ ) and local standard deviation ( $\sigma_t$ $σ_{t}$ ). It employs a dynamic threshold coefficient ( $k$ $k$ ) that adapts to the global fluctuation level of the sequence.
  - Low-volatility sequences use a strict threshold ( $k=2.5$ ).
  - Medium-volatility sequences use a conventional threshold ( $k=3.0$ ).
  - High-volatility sequences use a loose threshold ( $k=3.5$ ).
- Smoothing: Instead of eliminating extreme values, the algorithm applies weighted average smoothing ( $x'_t = \alpha \cdot \mu_t + (1-\alpha) \cdot x_t$ ) to preserve trend characteristics while reducing noise interference.
Fluctuation-Aware Dynamic Sparse Attention (FADSA):
- Objective: To replace the random ProbSparse sampling with a data-driven strategy that prioritizes highly volatile subsequences.
- Mechanism: After denoising, the cost sequence is partitioned into windows. The standard deviation of each subsequence is calculated and normalized to generate a sampling weight ( $w_i$ ).
- Dual-Mechanism Sampling:
  - Weighted Probability Sampling: 80% of the query samples are selected based on the fluctuation weights, biasing the attention toward high-volatility regions.
  - Forced Retention: The top 20% of highly volatile subsequences are forcibly included in the sampling to ensure key fluctuation information is not randomly discarded.
- Outcome: This ensures the model allocates more attention resources to dynamic cost segments while maintaining the $O(L \log L)$ computational complexity of the original Informer.

Key Contributions

Adaptive Preprocessing: Introduction of a dynamic denoising algorithm that adjusts thresholds based on global and local statistical features, effectively balancing noise removal with the retention of critical cost shock information.
Volatility-Aware Attention: Development of a FADSA mechanism that couples subsequence fluctuation indicators with the attention sampling strategy, addressing the "feature weakening" issue of random sampling in volatile cost data.
Collaborative Optimization: Demonstration of a "denoising–attention compensation" mechanism where preprocessing stabilizes the data foundation, and the attention mechanism compensates for potential information loss by focusing on high-value fluctuations.

Experimental Results
The model was validated on a real-world enterprise cost dataset and the ETT (Electricity Transformer Temperature) benchmark dataset.

Performance on Enterprise Cost Data:
- 12-Step Prediction: The proposed model achieved an MSE of 0.3819 and MAE of 0.3449. Compared to a model using only the denoising algorithm (COSTP), this represents a reduction of 2.1% in MSE and 2.2% in MAE.
- 24-Step Prediction: The model achieved an MSE of 0.5035 and MAE of 0.4202, showing reductions of 0.1% and 0.2% respectively compared to the denoising-only baseline.
- Observation: The improvements are most pronounced in medium-term predictions (12 and 24 steps), which are critical for strategic cost control. Short-term predictions (6 steps) showed minimal gains, as denoised data alone suffices for simple short-term trends.
Stability: The proposed model demonstrated superior stability compared to the original Informer and denoising-only variants, avoiding the "false low errors" caused by learning spurious noise patterns.

Significance and Claims
The authors claim that this study offers both theoretical and engineering value:

Theoretical: It enriches the optimization directions of the Informer model specifically for cost forecasting, providing new insights into handling time series with high noise and high volatility. It offers a novel solution to the LSTF problem by integrating fluctuation-aware sampling.
Engineering: The improved model provides more accurate medium-term trend references for enterprise cost control. By enabling early warnings of potential overspending points and facilitating timely risk mitigation, the method supports strategic cost management and improves resource allocation efficiency.
Future Work: The authors note that future research will aim to incorporate external influencing factors (e.g., raw material prices, market supply/demand, policy changes) to build a multi-factor prediction framework and extend these adaptive strategies to other Informer-based models.

The Problem: When the Data Goes Wild

The Solution: A Smarter, More Attentive Librarian

What They Found: Better Predictions for the Middle Term

Why This Matters

Technical Summary: Research on Enterprise Cost Prediction Method Based on Improved Informer Model

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