Leveraging Diffusion Transformers for Stock Factor Augmentation in Financial Markets

Comment 3: Will generated data be useful in classification and DRL task?

Thanks for the great question. We believe DiffsFormer is intended to address the data scarcity problem, and may be helpful to many problem or approaches may face with the sparse data problem, with modest changes. Hence we believe DiffsFormer could have a quite broad impact and applications.

However, as for the two tasks you mentioned:

(1) We believe direction prediction faces with the scarcity problem as we share the same input data type, hence Diffsformer may help with the direction prediction task from this perspective. However, since the label for direction prediction problem is binary, we may assume that it may have a higher demand for feature-label matching. Although DiffsFormer uses the original label for the generated feature which alleviates the problem and works for the regression task, we are not sure if it works for the classification task. We believe if a better strategy is developed to ensure the exact match of feature and label, our method would be able to help the classification problem.

(2) We are not familiar with the Deep Reinforcement Learning approaches. We think this task requires expert knowledge in reward design, policy selection and rich experience in optimization to which we lack the capacity. Our strategy now is simple: a money-weighted position over the predicted top-30 stocks. We believe DRL in portfolio management may require the accurate prediction of the return of each stock where we can help, but currently it is not within our scope.

We've discussed these two tasks in the limitation section in around Line 533. We would like to emphasize that our work offers valuable insights to the field, and our contribution is significant and substantial.

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Comment 4: Lack of qualitative results to demonstrate the ability to condition the generation process.

We fully agree that qualitative results are important to intuitively show the effect of the proposed approach. Due to page limit, we've arranged it to Figure 10 in Appendix E.1. We've thought about plotted different time-series to demonstrate the effects. However, our task is a cross-sectional generation task (multivariate time-series generation tasks with 158 dimensions) which is difficult to visualize ana analyze through different timeseries. Instead, we provide a qualitative result with t-SNE. Each sample in the plot is a projection of a 8*158 sequence. We can see from figure (a) that if we generate without editing, the distribution of the original and generated features deviate; however, from figure (c) if we edits the sample with conditioning and transfer learning methods, the augmented feature are generated by perturbing the original feature, hence two distributions are aligned.

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Summary

We are grateful for your positive evaluation of our motivation, presentation and effectiveness. We further provide the following responses:

• More baselines
• More test metrics
• Limitation discussion
• Qualitative result clarification We hope our responses address your concerns. Overall, we believe our work makes good contributions, and we would appreciate your reconsideration. Thank you for your efforts again!

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[1] Wiese, Magnus, et al. "Quant GANs: deep generation of financial time series." Quantitative Finance 20.9 (2020): 1419-1440.

[2] Seyfi, Ali, Jean-Francois Rajotte, and Raymond Ng. "Generating multivariate time series with COmmon Source CoordInated GAN (COSCI-GAN)." Advances in neural information processing systems 35 (2022): 32777-32788.

[3] Desai et al. TimeVAE: A Variational Auto-Encoder for Multivariate Time Series Generation.

[4] Kollovieh, Marcel, et al. "Predict, refine, synthesize: Self-guiding diffusion models for probabilistic time series forecasting." Advances in Neural Information Processing Systems 36 (2024).

[5] Xia, Haochong, et al. "Market-GAN: Adding Control to Financial Market Data Generation with Semantic Context." Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 38. No. 14. 2024.

Line 265: I didn't understand the following sentence for a long time: Since our labels are continuous rather than discrete, we refer to this mechanism as “predictor-free guidance.” After reading the reference (Ho, Salimans, 2022) I realized that this name follows the "classifier-free guidance" in that paper. But the present paper didn't make it clear.

Sorry for not making the term clear. We've reformulated this sentence in line 296 as you suggested.

What's CSIS in Table 4?

Thanks for the constructive question. CSIS are all of the stocks in China A-share market. We've added the concept in line 245 and line 477 in Table 4 Caption.

The metric values of Excess Return (ER) in Tables 1 and 2 are the same as the Return Ration (RR) in Tables 8 and 9. Please explain.

Sorry for the confusions made. ER is the same as RR and it is a typo. As statistics in Tables are identical, we've deleted them in the Table 8 and 9 locating in Appendix to make it clear.

The authors are suggested to create a clear roadmap of the paper structure early on, ensure all figures are properly referenced and explained in order, and provide more explicit definitions of key concepts and variables used throughout.

We've clearly added a roadmap in introduction, which help let readers know the contribution of the papers and where to find corresponding techniques near the end of the introduction in Line 087 ~ Line 104.

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Comment 2: It's suggested the authors show the results with different T'. What values were used for T and T' for reporting the results in the paper?

We fully agree with you that T' is an important hyper-parameter in our work. Actually, we report the performance of different T' in Table 3, (a wrap table that may be overlooked, hence we've highlighted it with color). We choose T as 1000, following normal DM setting, and T' is chosen as 300 according to Table 3. BTW, a more detailed table is reported in Table 6 could help the reproduction of our work.

Furthermore, besides T', we've added a summarization our contribution in Line 105:

• We reveal the importance of data augmentation in the context of stock forecasting and explore the use of diffusion stock transformer (DiffsFormer for short) to address data scarcity.

• The framework integrates transfer learning to leverage knowledge from other markets, alleviating the difficulty of training DMs on sparse data. Additionally, the edit mechanism could obtain new features with original label with optimized efficiency, enabling training of the downstream forecasting task. For better alignment of the feature and the original label, we propose to employ excess return as the conditioning to enhance the relationship between them. Inspired by classfier-free guidance, a flexible predictor-free guidance approach is integrated as excess return is continuous rather than discrete.

• We verify the effectiveness of DiffsFormer augmented training in CSI300 and CSI800 with nine commonly used machine learning models.

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Comment 3: It’s puzzling that many methods show lower IC after applying data augmentation

As suggested by Reviewer $\color{purple}{\text{14Ku}}$, we added the experiment for MSE and RMSE in Figure 6 in Line 432 ~ Line 443. Upon review, we find MSE, RMSE have similar trends to IC and RankIC: our model performs differently on different degrees of price fluctuation: it performs better on high-volatility stocks (top stocks and bottom stocks), however performs worse on low-volatility stocks (whose excess return is close to zero). We attribute the reason to the choice of target domain and source domain. The target domain consists of the largest 300 stocks in China A-share, these stocks are more established companies with stable earnings, hence tend to have lower volatility; the source domain consists of all of the stocks in China A-share, which means the source domain have a higher volatility than the target domain. Hence distilling knowledge from source domain to target domain enhances the prediction ability of high-volatility stocks at the expense of the low-volatility stocks, and since our strategy is choosing top30 stocks, this property is promising and leads to higher profit. This discussion has been added in Line 377 ~ Line 407.

Comment 4: The time efficiency improvement is rather unnecessary and can be incorrect.

Thanks for the question, and we believe there is a misunderstanding.

If we define T as the total diffusion step during forward process, the training Loop for diffusion models could be like:

• Sample real data $x_{0}$ from the training dataset
• Sample a random timestep t from {0, 1, ..., T-1} or {1, ..., T}
• Add noise to $x_0$ to create $x_t$
• Pass $x_t$ and t through the neural network
• Compute loss between predicted and actual noise

As you mentioned, the length of the entire time horizion matters, as it affects the value of $\alpha_t$ and $\beta_t$. Hence in our method, we remain T=1000 and initialize the $\alpha_t$ and $\beta_t$. Since we only perturb seed point for T' << T steps then reverse, we believe $p_{\theta}(x_{t−1}|x_{t})$ will not be used for t larger than T'. In our paper, we set T'= 300. From the training loop, we could observe the probability of choosing specific t < T is 1/999, and choosing specific t < T' is 1/299. In other words, for the same training epochs, the probability of selecting useful timestep increased to more than three times the original after decreasing the candidate set size from T to T'. Although theoretical time complexity doesn't change, the convergence speed becomes faster and real training time decreases. Figure 9 reflects the phenomenon. We've added more clarification in Section 3.2 in Line 284. Hope that the misunderstanding is mitigated!

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Comments 5:

- Technical concepts of DM are not very well written or in some cases misleading or incorrect;

- the variables and other quantities related to stock market prediction isn't very well explained;

- stock factors in return ratio are used throughout the introduction section even though they are defined in section 2;

- The terms like SNR and data homogeneity should have been properly defined in mathematical terms.

We greatly appreciate your observations and would be most grateful if you could kindly provide some specific examples to help us address your concerns more effectively:

• Regarding the technical concepts of diffusion models, most of the papers follow the same formulation. There might be some typos in our equations that makes you feel wrong. Could you please point out which particular sections or statements you found potentially inaccurate? This would be immensely helpful in our revision process.
• In around Line 182 Diffusion Process, we've introduced the variables and other quantities about input data. Besides, we've used almost one page to introduce the background of the task. If there are more specific variables you feel require more clarification, please indicate and we're more than happy to explain them in the manuscript.
• We apologize for any confusion caused by the use of terms like "stock factors" and "return ratio" in the introduction. We have given text explanations and refer readers who are unfamiliar to the concepts to Section 2 in Line 36 and Line 47.
• Your point about SNR is well-taken. We've defined SNR in mathematical terms in Section 2 in Line 125 ~ Line 128. As for data homogeneity, it is a qualitative concept rather than a quantitative one. Many metrics such as variance, entropy, cosine similarity could serve as an indicator of the homogeneity property.

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Comments 6: Lastly, I feel like this paper being very specific in its application should be submitted in a domain specific conference and perhaps not a very good fit for ICLR.

We acknowledge that our work is a economic-specific application paper. And we believe that our paper is a good fit for domain specific conference. However, we would like to kindly remind that:

In call for paper page (https://iclr.cc/Conferences/2025/CallForPapers), the subject area for ICLR 2025 is: "We consider a broad range of subject areas including feature learning, metric learning, compositional modeling, structured prediction, reinforcement learning, uncertainty quantification and issues regarding large-scale learning and non-convex optimization, as well as applications in vision, audio, speech, language, music, robotics, games, healthcare, biology, sustainability, economics, ethical considerations in ML, and others."

As our paper aims to do feature learning (data augmentation) from a representation learning perspective, we believe our paper is a good fit for ICLR.

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Summary

We are grateful for your positive evaluation of our motivation. We further provide the following responses:

• An in-depth discussion about novelty.
• Revise our manuscript to enhance reading experience.

We hope our responses address your concerns. Overall, we believe our work makes good contributions, and we would appreciate your reconsideration. Thank you for your efforts again!

Comments 5: latest state-of-the-art models in the domain of stock forecasting

Thanks for the suggestion. HIST [1] is one of the SOTA model that submitted their codes to https://github.com/microsoft/qlib. Moreover, we have added a comparison with the MTMD [2] model. Our current comparison was carefully conducted within the same time frame in the paper. The new results has been added to Table 1, 2, and 8.

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Comments 6: Alternative augmentation strategies serve as a competitive baseline

Thanks for the advice. As suggested by Reviewer $\color{purple}{\text{14Ku}}$, we have added [3~5] as our baselines to the paper, please refer to Figure 8 around Line 490.

However, we find these baselines:

(1) cannot generate (feature, label) pairs. If original labels serve as the supervison signal for the generated feature, the performance drops. (2) cannot generate multivariate time-series data. Our cross-sectional data contains 158 factors, if we treat this multivariate sequence as 158 univariate sequences and generate them separately, the performance will face a significant drop since we overlook the correlation between features.

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Summary

We are grateful for your positive evaluation of our presentation, novelty, and effectiveness. We further provide the following responses:

• An in-depth discussion about generalization and Overfitting.
• Additional experiments in stock forecasting and data augmentation.
• Feature Importance. We hope our responses address your concerns. Overall, we believe our work makes good contributions, and we would appreciate your reconsideration. Thank you for your efforts again!

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[1] Xu et al. HIST: A Graph-based Framework for Stock Trend Forecasting via Mining Concept-Oriented Shared Information.

[2] Wang et al. MTMD: Multi-Scale Temporal Memory Learning and Efficient Debiasing Framework for Stock Trend Forecasting.

[3] Seyfi, Ali, Jean-Francois Rajotte, and Raymond Ng. "Generating multivariate time series with COmmon Source CoordInated GAN (COSCI-GAN)." Advances in neural information processing systems 35 (2022): 32777-32788.

[4] Wiese, Magnus, et al. "Quant GANs: deep generation of financial time series." Quantitative Finance 20.9 (2020): 1419-1440.

[5] Desai et al. TimeVAE: A Variational Auto-Encoder for Multivariate Time Series Generation.

Dear Reviewer $\color{blue}{\text{ZDKm}}$,

We have carefully checked our rebuttal. We guess you might be concerned about our answers about feature importance discussion about LIME. We hereby provide with the full LIME result and the explanation for the top-5 feature we got.

101_t-7 <= -0.34: 0.030

156_t-7 <= -0.70: 0.021

146_t-7 <= -0.70: -0.020

137_t-7 > 0.90: 0.019

11_t-6 <= -0.94: -0.018

0 < 11_t-7 <= 0.56: 0.016

67_t-7 <= -0.66: -0.015

43_t-7 <= -0.57: 0.015

101_t-6 <= -0.34: 0.014

132_t-7 > 0.79: -0.013

29_t-7 <= -0.67: 0.013

100_t-6 <= -0.67: 0.013

14_t-7 > 0.66: -0.013

151_t-7 > 0.70: -0.012

152_t-7 > 0.72: 0.012

9_t-5 <= -0.68: 0.012

52_t-7 > 0.6: 0.012

100_t-7 <= -0.67: 0.012

26_t-7 <= -0.58: 0.012

140_t-7 > 0.83: 0.012

110_t-6 <= -0.67: 0.012

10_t-1 <= -0.57: -0.011

52_t-6 > 0.6: 0.011

110_t-7 <= -0.67: 0.011

5_t-6 <= -0.57: -0.011

59_t-5 <= -0.92: -0.011

156_t-6 > 0.64: -0.011

-0.57 < 5_t-7 <= 0: -0.011

51_t-7 > 0.58: 0.011

8_t-7 > 0.64: -0.010

0 < 98_t-7 <= 0.67: 0.010

-0.54 < 112_t-0 <= 0: 0.010

26_t-6 <= -0.58: 0.010

81_t-7 > 0.81: -0.010

101_t-5 <= -0.34: 0.010

146_t-5 > 0.63: 0.010

0 < 78_t-7 <= 0.67: 0.010

49_t-7 > 0.58: 0.009

0.01 < 49_t-4 <= 0.59: 0.009

42_t-5 > 0.65: -0.009

26_t-5 <= -0.58: 0.009

97_t-6 > 0.62: 0.009

141_t-6 > 0.85: -0.009

9_t-6 <= -0.68: 0.009

70_t-7 <= -0.66: -0.009

119_t-7 > 0.69: 0.009

61_t-7 > 0.54: 0.009

96_t-7 > 0.61: 0.009

58_t-5 <= -1.04: 0.009

134_t-6 <= -0.57: -0.009

95_t-6 > 0.6: -0.008

111_t-7 <= -0.67: 0.008

138_t-6 > 0.74: 0.008

-0.71 < 156_t-3 <= -0.01: 0.008

84_t-7 <= -0.67: 0.008

-0.67 < 110_t-0 <= 0: 0.008

124_t-7 <= -0.69: -0.008

153_t-0 <= -0.73: -0.008

3_t-7 <= -0.57: 0.008

134_t-5 <= -0.57: -0.008

26_t-2 <= -0.58: 0.008

0 < 110_t-2 <= 1.01: -0.008

139_t-7 > 0.79: 0.008

102_t-7 <= -0.67: -0.008

156_t-5 > 0.63: -0.007

0_t-6 > 0.69: 0.007

0 < 57_t-0 <= 0.91: -0.007

108_t-2 > 0.67: 0.007

-0.01 < 126_t-2 <= 0.64: -0.007

39_t-7 > 0.65: 0.007

10_t-5 <= -0.57: -0.007

-0.01 < 37_t-2 <= 0.61: -0.007

143_t-6 > 0.63: -0.007

-0.61 < 4_t-5 <= 0: 0.007

9_t-4 > 0.63: -0.007

-0.61 < 15_t-1 <= 0: 0.007

12_t-5 <= -0.64: -0.007

141_t-7 > 0.85: -0.007

100_t-4 <= -0.67: 0.007

10_t-7 <= -0.57: -0.007

-0.69 < 116_t-7 <= -0.01: 0.007

8_t-0 <= -0.69: 0.007

-0.74 < 36_t-3 <= -0.01: 0.007

6_t-7 > 0.80: -0.007

146_t-6 > 0.64: 0.007

123_t-5 > 0.64: -0.007

9_t-3 <= -0.68: 0.007

86_t-7 <= -0.6: -0.007

11_t-5 <= -0.94: -0.007

0 < 140_t-2 <= 0.82: 0.007

-0.69 < 123_t-7 <= 0: 0.007

-0.67 < 106_t-5 <= 0: -0.007

74_t-7 <= -0.67: -0.007

-0.6 < 4_t-2 <= 0: 0.007

0 < 131_t-7 <= 0.76: 0.006

0 < 112_t-3 <= 0.67: -0.006

0 < 6_t-5 <= 0.8: 0.006

0 < 64_t-4 <= 0.9: -0.006

81_t-4 > 0.81: -0.006

25_t-0 <= -0.59: -0.006

43_t-6 <= -0.57: 0.006

109_t-3 > 0.67: 0.006

129_t-0 > 0.74: -0.006

155_t-4 > 0.63: 0.006

-0.01 < 37_t-7 <= 0.61: 0.006

27_t-4 <= -0.58: 0.006

0 < 136_t-0 <= 0.91: -0.006

0 < 99_t-4 <= 0.67: 0.006

-0.86 < 60_t-0 <= 0.01: 0.006

99_t-2 > 0.67: 0.006

83_t-7 <= -0.67: -0.006

156_t-4 > 0.63: -0.006

-0.56 < 47_t-6 <= 0: -0.006

-0.63 < 148_t-7 <= 0: 0.006

85_t-1 <= -0.67: -0.005

1_t-0 <= -0.59: -0.005

130_t-4 <= -0.6: 0.005

-0.67 < 78_t-5 <= 0: -0.005

-0.54 < 112_t-6 <= 0: 0.005

1_t-6 > 0.86: 0.005

96_t-6 > 0.61: 0.005

-0.69 < 113_t-7 <= 0: -0.005

131_t-6 <= -0.6: -0.005

78_t-0 <= -0.67: -0.005

-0.81 < 90_t-7 <= 0: 0.005

-0.68 < 30_t-7 <= 0: 0.005

136_t-5 <= -0.57: -0.005

-0.01 < 115_t-3 <= 0.64: 0.005

96_t-1 > 0.6: 0.005

0 < 44_t-7 <= 0.89: -0.005

44_t-1 <= -0.57: 0.005

-0.67 < 29_t-6 <= 0: 0.005

-0.67 < 106_t-3 <= 0: 0.005

-0 < 143_t-3 <= 0.62: 0.005

92_t-3 > 0.6: 0.005

86_t-4 <= -0.6: -0.005

-0 < 69_t-0 <= 0.67: 0.005

39_t-6 > 0.65: 0.005

93_t-6 > 0.57: -0.005

89_t-4 > 0.59: -0.005

150_t-4 <= -0.63: 0.005

-0 < 89_t-2 <= 0.59: 0.005

0.02 < 50_t-1 <= 0.59: 0.005

-0.67 < 83_t-1 <= 0: -0.005

0 < 71_t-5 <= 0.69: 0.005

149_t-6 <= -0.64: 0.004

147_t-0 <= -0.72: 0.004

-0.81 < 90_t-6 <= 0: 0.004

-0.74 < 35_t-6 <= -0: 0.004

71_t-7 <= -0.64: -0.004

-0.58 < 24_t-0 <= -0.02: -0.004

-0.01 < 114_t-0 <= 0.64: -0.004

-0.71 < 155_t-3 <= -0.01: -0.004

-0.74 < 36_t-0 <= -0.01: 0.004

64_t-5 > 0.9: -0.004

85_t-6 <= -0.67: -0.003

0 < 93_t-4 <= 0.57: -0.003

-0.57 < 136_t-4 <= 0: -0.003

The top 5 features are:

1. Count Positive-20: the average number of times the closing price was higher than the previous day's close over last 20 days.
2. Volume Sum Difference-20: the difference between the number of volume increases and volume decreases over last 20 days.
3. Volume Sum Positive-30: the proportion of volume increases over last 30 days.
4. Standard deviation of volume-20: the standard deviation of volume over last 20 days.
5. Highest price for the last day.

Hope it addresses your concern. If there is any remaining concerns, please feel free to tell us and we are always more than happy to discuss.

Best regards,

Submission 8851 Authors