Title: Transparent Networks for Multivariate Time Series
Venue: NeurIPS 2024
Accepted: no
Keywords: Generalized Additive Models

Interpretability

Time Series

Transparent Model
Abstract: Transparent models, which are machine learning models that produce inherently interpretable predictions, are receiving significant attention in high-stakes domains. However, despite much real-world data being collected as time series, there is a lack of studies on transparent time series models. To address this gap, we propose a novel transparent neural network model for time series called Generalized Additive Time Series Model (GATSM). GATSM consists of two parts: 1) independent feature networks to learn feature representations, and 2) a transparent temporal module to learn temporal patterns across different time steps using the feature representations. This structure allows GATSM to effectively capture temporal patterns and handle dynamic-length time series while preserving transparency. Empirical experiments show that GATSM significantly outperforms existing generalized additive models and achieves comparable performance to black-box time series models, such as recurrent neural networks and Transformer. In addition, we demonstrate that GATSM finds interesting patterns in time series. The source code is available at https://anonymous.4open.science/r/GATSM-78F4/.

1

Abstract

Transparent models, which are machine learning models that produce inherently interpretable predictions, are receiving significant attention in high-stakes domains. However, despite much real-world data being collected as time series, there is a lack of studies on transparent time series models. To address this gap, we propose a novel transparent neural network model for time series called Generalized Additive Time Series Model (GATSM). GATSM consists of two parts: 1) independent feature networks to learn feature representations, and 2) a transparent temporal module to learn temporal patterns across different time steps using the feature representations. This structure allows GATSM to effectively capture temporal patterns and handle dynamic-length time series while preserving transparency. Empirical experiments show that GATSM significantly outperforms existing generalized additive models and achieves comparable performance to black-box time series models, such as recurrent neural networks and Transformer. In addition, we demonstrate that GATSM finds interesting patterns in time series. The source code is available at https://anonymous.4open.science/r/GATSM-78F4/ .

1 Introduction

Artificial neural networks excel at learning complex representations and demonstrate remarkable 17 predictive performance across various fields. However, their complexity makes interpreting the 18 decision-making processes of neural network models challenging. Consequently, post-hoc explainable 19 artificial intelligence (XAI) methods, which explain the predictions of trained black-box models, 20 have been widely studied in recent years [1, 2, 3, 4]. XAI methods are generally effective at 21 providing humans with understandable explanations of model predictions. However, they may 22 produce incorrect and unfaithful explanations of the underlying black-box model and cannot provide 23 actual contributions of input features to model predictions [5, 6]. Therefore, their applicability to 24 high-stakes domains-such as healthcare and fraud detection, where faithfulness to the underlying 25 model and actual contributions of features are important-is limited. 26

Due to these limitations, transparent (i.e., inherently interpretable) models are attracting attention as 27

alternatives to XAI in high-stakes domains [7, 8, 9]. Modern transparent models typically adhere to 28

the generalized additive model (GAM) framework [10]. A GAM consists of independent functions, 29

each corresponding to an input feature, and makes predictions as a linear combination of these 30

functions (e.g., the sum of all functions). Therefore, each function reflects the contribution of its 31

32

respective feature. For this reason, interpreting GAMs is straightforward, making them widely used in

various fields, such as healthcare [11, 12], survival analysis [13], and model bias discovery [7, 14, 15]. 33

However, despite much real-world data being collected as time series, research on GAMs for time 34

series remains scarce. Consequently, the applicability of GAMs in real-world scenarios is still limited. 35

To overcome this limitation, we propose a novel transparent model for multivariate time series 36

called Generalized Additive Time Series Model (GATSM). GATSM consists of independent feature 37

networks to learn feature representations and a transparent temporal module to learn temporal patterns. 38

Since employing distinct networks across different time steps requires a massive amount of learnable 39 parameters, the feature networks in GATSM share the weights across all time steps, while the 40 temporal module independently learns temporal patterns. GATSM then generates final predictions by 41 integrating the feature representations with the temporal information from the temporal module. This 42 strategy allows GATSM to effectively capture temporal patterns and handle dynamic-length time 43 series while preserving transparency. Additionally, this approach facilitates the separate extraction of 44 time-independent feature contributions, the importance of individual time steps, and time-dependent 45 feature contributions through the feature functions, temporal module, and final prediction. To 46 demonstrate the effectiveness of GATSM, we conducted empirical experiments on various time series 47 datasets. The experimental results show that GATSM significantly outperforms existing GAMs 48 and achieves comparable performances to black-box time series models, such as recurrent neural 49 networks and Transformer [16]. In addition, we provide visualizations of GATSM's predictions to 50 demonstrate that GATSM finds interesting patterns in time series. 51

52

2 Related Works

Various XAI studies have been conducted over the past decade [7, 8, 9, 17, 18]; however, they are 53 less relevant to the transparent model that is the subject of this study. Therefore, we refer readers to 54 [19, 20] for more detailed information on recent XAI research. In this section, we review existing 55 transparent models closely related to our GATSM and discuss their limitations. 56

The simple linear model is designed to fit the conditional expectation g ( E ( y | x )) = ∑ M i =1 x i w i , 57 where g ( · ) is a link function, M indicates the number of input features, y is the target value for the 58 given input features x ∈ R M , and w i ∈ R is the learnable weight for x i . This model captures only 59 linear relationships between the target y and the inputs x . To address this limitation, GAM [10] 60 extends the simple linear model to the generalized form as follows: 61

where each f i ( · ) is a function that models the effect of a single feature, referred as a feature function. 62 Typically, f i ( · ) becomes a non-linear function such as a decision tree or neural network to capture 63 non-linear relationships. 64

Originally, GAMs were fitted via the backfitting algorithm using smooth splines [10, 21]. Later, Yin 65 Lou et al. [22] and Harsha Nori et al. [23] have proposed boosted decision tree-based GAMs, which 66 use boosted decision trees as feature functions. Spline- and tree-based GAMs have less flexibility 67 and scalability. Thus, extending them to transfer or multi-task learning is challenging. To overcome 68 this problem, various neural network-based GAMs have been proposed in recent years. Potts [24] 69 introduced generalized additive neural network, which employs 2-layer neural networks as feature 70 functions. Similarly, Rishabh Agarwal et al. [7] proposed neural additive model (NAM) that employs 71 multi-layer neural networks. To improve the scalability of NAM, Chun-Hao Chang et al. [8] and 72 Filip Radenovic et al. [9] proposed the neural oblivious tree-based GAM and the basis network-based 73 GAM, respectively. Xu et al. [25] introduced a sparse version of NAM using the group LASSO. One 74 disadvantage of GAMs is their limited predictive power, which stems from the fact that they only 75 learn first-order feature interactions-i.e., relationships between the target value and individual features. 76 To address this, various studies have been conducted to enhance the predictive powers of GAMs by 77 incorporating higher-order feature interactions, while still maintaining transparency. GA 2 M[26] 78 simply takes pairwise features as inputs to learn pairwise interactions. GAMI-Net [27], a neural 79 network-based GAM, consists of networks for main effects (i.e., first-order interactions) and pairwise 80 interactions. To enhance the interpretability of GAMI-Net, the sparsity and heredity constraints are 81 added, and trivial features are pruned in the training process. Sparse interaction additive network [28] 82

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is a 3-phase method for exploiting higher-order interactions. Initially, a black-box neural network is 83

trained; subsequently, the topk important features are identified using explainable feature attribution 84

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methods like LIME [1] and SHAP [2], and finally, NAM is trained with these extracted features.

Dubey et al. [29] introduced scalable polynomial additive model, an end-to-end model that learns 86

higher-order interactions via polynomials. Similarly, Kim et al. [15] proposed higher-order NAM that 87

utilizes the feature crossing technique to capture higher-order interactions. Despite their capabilities, 88

the aforementioned GAMs cannot process time series data, which limits their applicability in real89

world scenarios. Recently, neural additive time series Model (NATM) [30], a time-series adaptation 90

of NAM, has been proposed. However, NATM handles each time step independently with separate 91

feature networks. This approach cannot capture effective temporal patterns and only takes fixed-length 92

time series as input. Our GATSM not only captures temporal patterns but also handles dynamic-length 93

time series. Table 1 shows the advantages of our GATSM compared to existing GAMs. 94

3 Problem Statement 95

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Wetackle the problem of the existing GAMs on time series. Equation (1) outlines the GAM framework for tabular data, which fails to capture the interactions between current and previous observations in time series. A straightforward method to extend GAM to time series, adopted in NATM, is applying

distinct feature functions to each time step and summing them to produce predictions: 99

where X ∈ R T × M is a time series with T time steps and M features, and t is the current time step. 100

This method can handle time series data as input but fails to capture effective temporal patterns 101

because the function f i,j ( · ) still does not interact with previous time steps. To overcome this problem, 102

we suggest a new form of GAM for time series defined as follows: 103

Definition 3.1 GAMs for time series, which capture temporal patterns hold the form of Equation 3 .

In Equation (3), the function f ( · , · ) can capture interactions between current and previous time steps. Therefore, GAMs adhering to Definition 3.1 are capable of capturing temporal patterns. However, implementing such a model while maintaining transparency poses challenges. In the following section, we will describe our approach to implementing a GAM that holds Definition 3.1. To the best of our knowledge, no existing literature addresses Definition 3.1.

4 Our Method: Generalized Additive Time Series Model

4.1 Architecture

Figure 1 shows the overall architecture of GATSM. Our model has two modules: 1) feature networks, called time-sharing neural basis model, for learning feature representations, and 2) masked multi-head attention for learning temporal patterns.

Time-Sharing NBM: Assume a time series with T time steps and M features. Applying GAMs to this time series necessitates T × M feature functions, which becomes problematic when dealing with large T or M due to increased model size. This limits the applicability of GAMs to real-world datasets. To overcome this problem, we extend neural basis model (NBM) [9] to time series as:

We refer to this extended version of NBM as time-sharing NBM. Time-sharing NBM has B basis functions, with each basis h k ( · ) taking a feature x i,j as input. The feature-specific weight w nbm j,k then projects the basis to the transformed feature ˜ x i,j . As depicted in Equation 4, the basis functions are shared across all features and time steps, drastically reducing the number of required feature functions T × M to B . We use B = 100 and implement h k ( · ) using multi-layer perceptron (MLP).

Masked MHA: GATSM employs multi-head attention (MHA) to learn temporal patterns. Although the dot product attention [16] is popular, simple dot operation has low expressive power [31]. Therefore, we adopt the 2-layer attention mechanism proposed by [31] to GATSM. We first transform ˜ x i = [˜ x i, 1 , ˜ x i, 2 , · · · , ˜ x i,M ] ∈ R M produced by Equation 4 as follows:

where Z ∈ R M × D is a learnable weight, pe i = [ pe i, 1 , pe i, 2 , · · · , pe i,D ] ∈ R D is the positional encoding for i -th step, and D indicates the hidden size. The positional encoding is defined as follows:

The positional encoding helps GATSM effectively capture temporal patterns. While learnable position 130 embedding also works in GATSM, we recommend positional encoding because position embedding 131 requires knowledge of the maximum number of time steps, which is often unknown in real-world 132 settings. After computing v i , we calculate the attention scores as follows: 133

where k is attention head index, σ ( · ) is an activation function, w attn k ∈ R 2 D , and m i,j ∈ R is the 134 mask value used to block future information. The time mask is defined as follows: 135

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Inference: The prediction of GATSM is produced by combining the transformed features from 136 time-sharing NBM with the attention scores from masked MHA. 137

where K is the number of attention heads, a k,t = [ a k,i, 1 , a k,i, 2 , · · · , a k,i,T ] ∈ R T is the attention map in Equation 8, ˜ X = [˜ x 1 , ˜ x 2 , · · · , ˜ x T ] ∈ R T × M is the transformed features in Equation 4, and w out k ∈ R M is the learnable output weight.

Interpretability: We can rewrite Equation 10 as the following scalar form:

Equation 11 shows that GATSM satisfying Definition 3.1. We can derive three types of interpretations from GATSM: 1) a k,t,u indicates the importance of time step u at time step t , 2) h b ( x t,m ) w nbm m,b w out k,m represents the time-independent contribution of feature m , and 3) a k,t,u h b ( x t,m ) w nbm m,b w out k,m represents the time-dependent contribution of feature m at time step t .

5 Experiments

5.1 Experimental Setup

Datasets: We conducted our experiments using eight publicly available real-world time series datasets. From the Monash repository [32], we sourced three datasets: Energy, Rainfall, and AirQuality. Another three datasets, Heartbeat, LSST, and NATOPS, were downloaded from the UCR repository [33]. The remaining two datasets, Mortality and Sepsis, were downloaded from the PhysioNet [34]. We perform ordinal encoding for categorical features and standardize features to have zero-mean and unit-variance. For forecasting tasks, target value y is also standardized to zero-mean and unit-variance. If the dataset contains missing values, we impute categorical features with their modes and numerical features with their means. The dataset is split into a 60%/20%/20% ratio for training, validation, and testing, respectively. Table 2 shows the statistics of the experimental datasets. Further details of the experimental datasets can be found in Appendix B.

FCST: forecasting

Baselines: We compare our GATSM with 12 baselines, which can be categorized into four groups: 1) Black-box tabular models include extreme gradient boosting (XGBoost) [35] and MLP. 2) Black-box time series models include simple recurrent neural network (RNN), gated recurrent unit (GRU), long short-term memory (LSTM), and Transformer [16]. 3) Transparent tabular models are simple linear model (Linear), explainable boosting machine (EBM) [23], NAM [7], NodeGAM [8], and NBM [9]. 4) NATM [30] is a transparent time series model.

Implementation: We implement XGBoost and EBM models using the xgboost and interpretml libraries, respectively. For NodeGAM, we employ the official implementation provided by its authors [8]. The remaining models are developed using PyTorch [36]. All models undergo hyperparameter

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tuning via Optuna [37]. The pytorch-based models are optimized with the Adam with decoupled weight decay (AdamW) [38] optimizer on an NVIDIA A100 GPU. Model training is halted if the validation loss does not decrease over 20 epochs. We use mean squared error for the forecasting tasks, and for classification tasks, we use cross-entropy loss. Further details of the model implementations and hyper-parameters are provided in Appendix C.

5.2 Comparison with baselines

Table 3 shows the predictive performances of the experimental models. We report mean scores and standard deviations over five different random seeds. For the forecasting datasets, we evaluate R 2 scores. For the binary classification datasets, we assess the area under the receiver operating characteristic curve (AUROC). For the multi-class classification datasets, we measure accuracy. We highlight the best-performing model in bold and underline the second-best model. Since the tabular models cannot handle time series, they only take x t to produce y t .

On the Energy and Heartbeat datasets, which are small in size, our GATSM demonstrates the best 179 performance, indicating strong generalization ability. EBM, XGBoost, and Transformer struggle 180 with overfitting on the Energy dataset. For the Mortality and Sepsis datasets, there is no significant 181 performance difference between tabular and time series models, nor between black-box and trans182 parent models. This suggests that these two healthcare datasets lack significant temporal patterns 183 and feature interactions. It is likely that seasonal patterns are hard to detect in medical data, and 184 the patient's current condition already encapsulates previous conditions, making historical data less 185 crucial. Since these datasets contain variable-length time series, the performance of NATM, which 186 can only handle fixed-length time series, is not available. On the Rainfall, AirQuality, LSST, and 187 NATOPS datasets, the time series models significantly outperform the tabular models, indicating 188 that these datasets contain important temporal patterns that tabular models cannot capture. Addition189 ally, the black-box models outperform the transparent models, suggesting that these datasets have 190 higher-order feature interactions that transparent models cannot capture. Nevertheless, GATSM is the 191 best model within the transparent model group and performs comparably to Transformer. Overall, 192 GATSM achieved the best average rank in the experiments, followed by the Transformer, indicating 193 GATSM's superiority. Additional experiments on model throughput and an ablation study on the 194 basis functions are presented in Appendix D. 195

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5.3 Ablation study

Choice of feature function: We evaluate the performance of GATSM by changing the feature functions using three models: Linear, NAM, and NBM. Table 4 presents the results of this experiment. The simple linear function performs poorly because it lacks the capability to capture non-linear relationships. In contrast, NAM, which can capture non-linearity, shows improved performance over the linear function. However, NBM stands out by achieving the best performance in six out of eight datasets. This indicates that the basis strategy of NBM is highly effective for time series data.

Design of temporal module: We evaluate the performance of GATSM by modifying the design of the temporal module. The results are presented in Table 5. GATSM without the temporal module (Base) fails to learn temporal patterns and shows poor performance in the experiment. GATSM with only positional encoding (Base + PE) also shows similar performance to the Base, indicating that positional encoding alone is insufficient for capturing effective temporal patterns. GATSM with only multi-head attention (Base + MHA) outperforms the previous two methods, demonstrating that the MHAmechanism is beneficial for capturing temporal patterns. Finally, our full GATSM (Base + PE + MHA) significantly outperforms the other methods, suggesting that the combination of PE and MHA creates a synergistic effect. Consistent with our previous findings in section 5.2, all four methods show similar performances on the Mortality and Sepsis datasets, which lack significant temporal patterns.

5.4 Interpretation

In this section, we visualize four interpretations of GATSM's predictions on the AirQuality dataset. In addition, interpretations for the Rainfall dataset can be found in Appendix E.

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Time-step importance: We plot the average attention scores at the last time step T in Figure 2. The process for extracting the average attention score of time step u at time step t is formalized as ∑ K k =1 a k,t,u . This process is repeated over all data samples, and the results are averaged. Based on Figure 2, it seems that GATSM pays more attention to the initial and last states than to the intermediate states. This indicates that the current concentration of particulate matter depends on the initial state.

Global feature contribution: Figure 3 illustrates the global behavior of features in the AirQuality dataset, with red bars indicating the density of training samples. We extract ∑ K k =1 h b ( x t,m ) w nbm m,b w out k,m from GATSM and repeat this process over the range of minimum to maximum feature values to plot the line. We found that the behavior of SO2 , O3 , and windspeed is inconsistent with prior human knowledge. Typically, high levels of SO2 and O3 are associated with poor air quality. However, GATSM learned that particulate matter concentration starts to decrease when SO2 exceeds 10 and O3 exceeds 5. This discrepancy may be due to sparse training samples in these regions, leading to insufficient training, or there may be interactions with other features. Another known fact is that high windspeed decreases particulate matter concentration. This is consistent when windspeed is below 0.7 in our observation. However, particulate matter concentration drastically increases when windspeed exceeds 0.7, likely due to the wind causing yellow dust.

Local time-independent feature contribution: To interpret the prediction of a data sample, we plot the local time-independent feature contributions, ∑ K k =1 h b ( x t,m ) w nbm m,b w out k,m , in Figure 4. The main x-axis (blue) represents feature contribution, the sub x-axis (red) represents feature value, and the y-axis represents time steps. We found that SO2 , NO2 , CO , and O3 have positive correlations. In contrast, temperature , pressure , dew point , and windspeed have negative correlations. These are consistent with the global interpretations shown in Figure 3. Rainfall has the same values across all time steps.

Local time-dependent feature contribution: We also visualize the local time-dependent feature contributions, ∑ K k =1 a k,t,u h b ( x t,m ) w nbm m,b w out k,m . Figure 5 illustrates the interpretation of the same data sample as in Figure 4. The time-dependent interpretation differs slightly from the time-independent interpretation. We found that there are time lags in SO2 , NO2 , CO , and O3 , meaning previous feature values affect current feature contributions. For example, in the case of SO2 , low feature values around time step 5 lead to low feature contributions around time step 13.

6 Future Works & Conclusion

Although GATSM achieved state-of-the-art performance within the transparent model category, it has several limitations. This section discusses these limitations and suggests future work to address them. GAMs have relatively slower computational times and larger model sizes compared to black-box models because they require the same number of feature functions as input features. To address this problem, methods such as the basis strategy can be proposed to reduce the number of feature functions, or entirely new methods for transparent models can be developed. The attention mechanism in GATSM may be a bottleneck. Fast attention mechanisms proposed in the literature [39, 40, 41, 42, 43], or the recently proposed Mamba [44], can help overcome this limitation. Existing time series models, including GATSM, only handle discrete time series and have limited length generalization ability, resulting in significantly reduced performance when very long sequences, unseen during training, are input. Extending GATSM to continuous models using NeuralODE [45] or HiPPO [46] could address this issue. GATSM still cannot learn higher-order feature interactions internally and shows low performance on complex datasets. Feature interaction methods proposed for transparent models may help address this problem [29, 15].

In this papre, we proposed a novel transparent model for time series named GATSM. GATSM consists of time-sharing NBM and the temporal module to effectively learn feature representations and temporal patterns while maintaining transparency. The experimental results demonstrated that GATSM has superior generalization ability and is the only transparent model with performance comparable to Transformer. We provided various visual interpretations of GATSM, demonstrated that GATSM capture interesting patterns in time series data. We anticipate that GATSM will be widely adopted in various fields and demonstrate strong performance. The broader impacts of GATSM across various fields can be found in Appendix A.

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References

Marco Tulio Ribeiro, Sameer Singh, and Carlos Guestrin. "Why Should I Trust You?": Explaining the Predictions of Any Classifier. In ACM SIGKDD International Conference on Knowledge Discovery and Data Mining , 2016.

Scott M. Lundberg and Su-In Lee. A Unified Approach to Interpreting Model Predictions. In 274 Advances in Neural Information Processing Systems , 2017. 275

Ramprasaath R. Selvaraju, Michael Cogswell, Abhishek Das, Ramakrishna Vedantam, Devi 276 Parikh, and Dhruv Batra. Grad-CAM: Visual Explanations From Deep Networks via Gradient277 Based Localization. 2017. 278

279

280

281

Ramaravind K. Mothilal, Amit Sharma, and Chenhao Tan. Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations. In Proceedings of the 2020 Conference on Fairness, Accountability, and Transparency , 2020.

282

283

284

285

286

287

288

289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

304

305

306

307

308

309

310

311

312

313

314

315

316

317

318

319

Cynthia Rudin. Please Stop Explaining Black Box Models for High Stakes Decisions. In Advances in Neural Information Processing Systems, Workshop on Critiquing and Correcting Trends in Machine Learning , 2018.

Cynthia Rudin. Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead. Nature Machine Intelligence , 1:206-215, May 2019.

Rishabh Agarwal, Levi Melnick, Nicholas Frosst, Xuezhou Zhang, Ben Lengerich, Rich Caruana, and Geoffrey E. Hinton. Neural Additive Models: Interpretable Machine Learning with Neural Nets. In Advances in Neural Information Processing Systems , 2021.

Chun-Hao Chang, Rich Caruana, and Anna Goldenberg. NODE-GAM: Neural Generalized Additive Model for Interpretable Deep Learning. In International Conference on Learning Representations , 2022.

Filip Radenovic, Abhimanyu Dubey, and Dhruv Mahajan. Neural Basis Models for Interpretability. In Advances in Neural Information Processing Systems , 2022.

Trevor Hastie and Robert Tibshirani. Generalized Additive Models. Statistical Science , 1(3): 297-318, August 1986.

Rich Caruana, Yin Lou, Johannes Gehrke, Paul Koch, Marc Sturm, and Noémie Elhadad. Intelligible Models for HealthCare: Predicting Pneumonia Risk and Hospital 30-day Readmission. In ACM SIGKDD International Conference on Knowledge Discovery and Data Mining , 2015.

Chun-Hao Chang, Sarah Tan, Ben Lengerich, Anna Goldenberg, and Rich Caruana. How Interpretable and Trustworthy are GAMs? In ACM SIGKDD International Conference on Knowledge Discovery and Data Mining , 2021.

Lev V. Utkin, Egor D. Satyukov, and Andrei V. Konstantinov. SurvNAM: The machine learning survival model explanation. Neural Networks , 147:81-102, March 2022.

Sarah Tan, Rich Caruana, Giles Hooker, and Yin Lou. Distill-and-Compare: Auditing BlackBox Models Using Transparent Model Distillation. In Proceedings of the 2018 AAAI/ACM Conference on AI, Ethics, and Society , 2018.

Minkyu Kim, Hyun-Soo Choi, and Jinho Kim. Higher-order Neural Additive Models: An Interpretable Machine Learning Model with Feature Interactions. arXiv preprint arXiv:2209.15409 , 2022.

Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Łukasz Kaiser, and Illia Polosukhin. Attention Is All You Need. In Advances in Neural Information Processing Systems , 2017.

Sebastian Bach, Alexander Binder, Grégoire Montavon, Frederick Klauschen, Klaus-Robert Müller, and Wojciech Samek. On Pixel-Wise Explanations for Non-Linear Classifier Decisions by Layer-Wise Relevance Propagation. PLoS ONE , 10(7), July 2015.

Avanti Shrikumar, Peyton Greenside, and Anshul Kundaje. Learning Important Features Through Propagating Activation Differences. In International Conference on Machine Learning , 2017.

Sajid Ali, Tamer Abuhmed, Shaker El-Sappagh, Khan Muhammad, Jose M. Alonso-Moral, 320 Roberto Confalonieri, Riccardo Guidotti, Javier Del Ser, Natalia Díaz-Rodríguez, and Francisco 321

322

323

324

325

326

327

328

329

330

331

332

333

334

335

336

337

338

339

340

341

342

343

344

345

346

347

348

349

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

372

373

374

375

Herrera. Explainable Artificial Intelligence (XAI): What we know and what is left to attain Trustworthy Artificial Intelligence. Information Fusion , 99:101805, November 2023.

Vikas Hassija, Vinay Chamola, Atmesh Mahapatra, Abhinandan Singal, Divyansh Goel, Kaizhu Huang, Simone Scardapane, Indro Spinelli, Mufti Mahmud, and Amir Hussain. Interpreting Black-Box Models: A Review on Explainable Artificial Intelligence. Cognitive Computation , 16(1):45-74, January 2024.

Grace Wahba. Spline Models for Observational Data . SIAM, September 1990.

Yin Lou, Rich Caruana, and Johannes Gehrke. Intelligible Models for Classification and Regression. In ACM SIGKDD International Conference on Knowledge Discovery and Data Mining , 2012.

Harsha Nori, Samuel Jenkins, Paul Koch, and Rich Caruana. InterpretML: A Unified Framework for Machine Learning Interpretability. arXiv preprint arXiv:1909.09223 , 2019.

William J. E. Potts. Generalized Additive Neural Networks. In ACM SIGKDD International Conference on Knowledge Discovery and Data Mining , 1999.

Shiyun Xu, Zhiqi Bu, Pratik Chaudhari, and Ian J. Barnett. Sparse Neural Additive Model: Interpretable Deep Learning with Feature Selection via Group Sparsity. In Joint European Conference on Machine Learning and Knowledge Discovery in Databases , 2023.

Yin Lou, Rich Caruana, Johannes Gehrke, and Giles Hooker. Accurate intelligible models with pairwise interactions. In ACM SIGKDD International Conference on Knowledge Discovery and Data Mining , 2013.

Zebin Yang, Aijun Zhang, and Agus Sudjianto. GAMI-Net: An Explainable Neural Network based on Generalized Additive Models with Structured Interactions. Pattern Recognition , 120: 108192, December 2021.

James Enouen and Yan Liu. Sparse Interaction Additive Networks via Feature Interaction Detection and Sparse Selection. Advances in Neural Information Processing Systems , 35, 2022.

Abhimanyu Dubey, Filip Radenovic, and Dhruv Mahajan. Scalable Interpretability via Polynomials. Advances in Neural Information Processing Systems , 2022.

Wonkeun Jo and Dongil Kim. Neural additive time-series models: Explainable deep learning for multivariate time-series prediction. Expert Systems with Applications , 228:120307, October 2023.

Petar Veliˇ ckovi´ c, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Liò, and Yoshua Bengio. Graph Attention Networks. In International Conference on Learning Representations , 2018.

Chang Wei Tan, Christoph Bergmeir, Francois Petitjean, and Geoffrey I. Webb. Monash University, UEA, UCR Time Series Extrinsic Regression Archive. arXiv preprint arXiv:2006.10996 , 2020.

Anthony Bagnall, Hoang Anh Dau, Jason Lines, Michael Flynn, James Large, Aaron Bostrom, Paul Southam, and Eamonn Keogh. The UEA multivariate time series classification archive, 2018. arXiv preprint arXiv:1811.00075 , 2018.

Ary L. Goldberger, Luis A. N. Amaral, Leon Glass, Jeffrey M. Hausdorff, Plamen Ch. Ivanov, Roger G. Mark, Joseph E. Mietus, George B. Moody, Chung-Kang Peng, and H. Eugene Stanley. PhysioBank, PhysioToolkit, and PhysioNet. Circulation , 101(23):e215-e220, June 2000.

Tianqi Chen and Carlos Guestrin. XGBoost: A Scalable Tree Boosting System. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining , 2016.

Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, Alban Desmaison, Andreas Kopf, Edward Yang, Zachary DeVito, Martin Raison, Alykhan Tejani, Sasank Chilamkurthy, Benoit Steiner, Lu Fang, Junjie Bai, and Soumith Chintala. PyTorch: An Imperative Style, High-Performance Deep Learning Library. In Advances in Neural Information Processing Systems , 2019.

Takuya Akiba, Shotaro Sano, Toshihiko Yanase, Takeru Ohta, and Masanori Koyama. Optuna: A Next-generation Hyperparameter Optimization Framework. In Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining , 2019.

Ilya Loshchilov and Frank Hutter. Decoupled Weight Decay Regularization. In International 376 Conference on Learning Representations , 2019. 377

378

379

380

Angelos Katharopoulos, Apoorv Vyas, Nikolaos Pappas, and François Fleuret. Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention. In International Conference on Machine Learning , 2020.

381

382

383

Lovish Madaan, Srinadh Bhojanapalli, Himanshu Jain, and Prateek Jain. Treeformer: Dense Gradient Trees for Efficient Attention Computation. In International Conference on Learning Representations , 2023.

Sinong Wang, Belinda Z. Li, Madian Khabsa, Han Fang, and Hao Ma. Linformer: Self-Attention 384 with Linear Complexity. arXiv preprint arXiv:2006.04768 , 2020. 385

386

387

388

389

Krzysztof Choromanski, Valerii Likhosherstov, David Dohan, Xingyou Song, Andreea Gane, Tamas Sarlos, Peter Hawkins, Jared Davis, Afroz Mohiuddin, Lukasz Kaiser, David Belanger, Lucy Colwell, and Adrian Weller. Rethinking Attention with Performers. In International Conference on Learning Representations , 2021.

390

391

392

393

Nikita Kitaev, Łukasz Kaiser, and Anselm Levskaya. Reformer: The Efficient Transformer. In International Conference on Learning Representations , 2020.

Albert Gu and Tri Dao. Mamba: Linear-Time Sequence Modeling with Selective State Spaces, 2023.

Ricky T. Q. Chen, Yulia Rubanova, Jesse Bettencourt, and David K Duvenaud. Neural Ordinary 394 Differential Equations. In Advances in Neural Information Processing Systems , 2018. 395

396

397

398

Albert Gu, Tri Dao, Stefano Ermon, Atri Rudra, and Christopher Ré. HiPPO: Recurrent Memory with Optimal Polynomial Projections. In Advances in Neural Information Processing Systems , 2020.

Eric J. Pedersen, David L. Miller, Gavin L. Simpson, and Noam Ross. Hierarchical generalized 399 additive models in ecology: an introduction with mgcv. PeerJ , 7:e6876, May 2019. 400

Trevor Hastie and Robert Tibshirani. Generalized additive models for medical research. Statisti401 cal Methods in Medical Research , 4(3):187-196, September 1995. 402

Appliances Energy Dataset, 2020. URL https://doi.org/10.5281/zenodo.3902637 . 403

Australia Rainfall Dataset, 2020. URL https://doi.org/10.5281/zenodo.3902654 . 404

Beijing PM10 Dataset, 2020. URL https://doi.org/10.5281/zenodo.3902667 . 405

Classification of Heart Sound Recordings: The PhysioNet/Computing in Cardiology Challenge 406 2016, 2016. URL https://physionet.org/content/challenge-2016/1.0.0/ . 407

Predicting Mortality of ICU Patients: The PhysioNet/Computing in Cardiology Challenge 2012, 408 2012. URL https://physionet.org/content/challenge-2012/1.0.0/ . 409

Early Prediction of Sepsis from Clinical Data: The PhysioNet/Computing in Cardiology Chal410 lenge 2019, 2019. URL https://physionet.org/content/challenge-2019/1.0.0/ . 411

PLAsTiCC Astronomical Classification, 2018. URL https://www.kaggle.com/c/ 412 PLAsTiCC-2018 . 413

AALTD'16 Time Series Classification Contest, 2016. URL https://aaltd16.irisa.fr/ 414 challenge/ . 415

Ignacio Oguiza. tsai - a state-of-the-art deep learning library for time series and sequential data. 416 Github, 2023. URL https://github.com/timeseriesAI/tsai . 417

Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. ImageNet Classification with Deep 418 Convolutional Neural Networks. In Advances in Neural Information Processing Systems , 2012. 419

Saining Xie, Ross Girshick, Piotr Dollar, Zhuowen Tu, and Kaiming He. Aggregated Residual 420 Transformations for Deep Neural Networks. In Proceedings of the IEEE Conference on 421 Computer Vision and Pattern Recognition , 2017. 422

James Bergstra, Rémi Bardenet, Yoshua Bengio, and Balázs Kégl. Algorithms for Hyper423 Parameter Optimization. In Advances in Neural Information Processing Systems , 2011. 424

Tri Dao, Daniel Y. Fu, Stefano Ermon, Atri Rudra, and Christopher Ré. FlashAttention: Fast 425 and Memory-Efficient Exact Attention with IO-Awareness. arXiv preprint arXiv:2205.14135 , 426 2022. 427

428

429

430

431

432

433

434

435

436

437

438

439

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A Broader impact 738

We discuss the expected impacts of GATSM across various fields. 739

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Time series adaptation: GATSM extends existing GAMs to time series, enabling tasks that traditional GAMs could not perform in this context - e.g., better performance on time series and finding temporal patterns.

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Improved decision-making system: GATSM can show users their exact decision-making process, providing trust and confidence in its predictions to users. This enables decision-makers to make more informed choices, crucial in high-stakes domains such as healthcare.

Ethical AI: GATSM can examine that their outcomes are biased or discriminatory by displaying the shape of feature functions. This is particularly important in ethically sensitive domains, such as recidivism prediction.

Scientific discovery: Transparent models have already been used in various research fields for scientific discovery [47, 48]. GATSM also can be applied to these domains to obtain novel scientific insights.

Despite these advantages, it is important to remember that the interpretations of transparent models do not necessarily reflect exact causal relationships. While transparent models provide clear and faithful interpretations, they are still not capable of identifying causal relationships. Causal discovery is a complex task that requires further research.

B Dataset details

We use eight publicly available datasets for our experiments. Three datasets - Energy, Rainfall, and 757 AirQuality - can be downloaded from the Monash repository [32]. Another three datasets - Heartbeat, 758 LSST, and NATOPS - are available from the UCR repository [33]. The remaining two datasets can 759 be downloaded from the PhysioNet [34]. Details of the datasets are provided below: 760

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Energy [49]: This dataset consists of 24 features related to temperature and humidity from sensors and weather conditions. These features are measured every 10 minutes. The goal of this dataset is to predict total energy usage.

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Rainfall [50]: This dataset consists of temperatures measured hourly. The goal of this dataset is to predict total daily rainfall in Australia.

AirQuality [51]: This dataset consists of features related to air pollutants and meteorological data. The goal of this dataset is to predict the PM10 level in Beijing.

Heartbeat [52]: This dataset consists of heart sounds collected from various locations on the body. Each sound was truncated to five seconds, and a spectrogram of each instance was created with a window size of 0.061 seconds with a 70% overlap. The goal of this dataset is to classify the sounds as either normal or abnormal.

Mortality [53] This dataset consists of records of adult patients admitted to the ICU. The input features include the patient demographics, vital signs, and lab results. The goal of this dataset is to predict the in-hospital death of patients.

Sepsis [54]: This dataset consists of records of ICU patients. The input features include patient demographics, vital signs, and lab results. The goal of this dataset is to predict sepsis six hours in advance at every time step.

LSST [55]: This challenge dataset aims to classify astronomical time series. These time series consist of six different light curves, simulated based on the data expected from the Large Synoptic Survey Telescope (LSST).

NATOPS [56]: This dataset aims to classify the Naval Air Training and Operating Procedures Standardization (NATOPS) motions used to control aircraft movements. It consists of 24 features representing the x, y, and z coordinates for each of the eight sensor locations attached to the body.

We used get_UCR_data() and get_Monash_regression_data() functions in the tsai library 784 [57] to load the UCR and Monash datasets. 785

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C Implementation details

We use 13 models, including GATSM, for our experiments. We implement XGBoost and EBM using the xgboost [35] and interpretml [23] libraries, respectively. For NodeGAM, we employ the official implementation provided by its authors [8]. The remaining models are developed using PyTorch [36]. In addition, we implement the feature functions in NAM and NBM using grouped convolutions [58, 59] to enhance their efficiency. XGBoost and EBM are trained on two AMD EPYC 7513 CPUs, while the other models are trained on an NVIDIA A100 GPU with 80GB VRAM. All models undergo hyperparameter tuning via Optuna [37] with the Tree-structured Parzen Estimator (TPE) algorithm [60] in 100 trials. The hyperparameter search space and the optimal hyperparameters for the models are provided below:

XGBoost: We tune the n_estimators in the integer interval [1, 1000], max_depth in the integer interval [0, 2000], learning rate in the continuous interval [1e-6, 1], subsample in the continuous interval [0, 1], and colsample_bytree in the continuous interval [0, 1].

MLP, NAM, NBM and NATM: We tune the batchnorm in the descret set {False, True}, dropout in the continuous interval [0, 0.9], learning_rate in the continuous interval [1e-3, 1e-2], and weight_decay in the continuous interval [1e-6, 1e-1] on a log scale.

RNN, GRU and LSTM: We tune the hidden_size in the integer interval [8, 128], dropout in the continuous interval [0, 0.9], learning_rate in the continuous interval [1e-3, 1e-2], and weight_decay in the continuous interval [1e-6, 1e-1] on a log scale.

Transformer: We tune the n_layers in the integer interval [1, 4], emb_size in the integer interval [8, 32], hidden_size in the integer interval [8, 128], n_heads in the integer interval [1, 8], dropout in the continuous interval [0, 0.9], learning_rate in the continuous interval [1e-3, 1e-2], and weight_decay in the continuous interval [1e-6, 1e-1] on a log scale.

Linear: We tune the learning_rate in the continuous interval [1e-3, 1e-2], and weight_decay in the continuous interval [1e-6, 1e-1] on a log scale.

EBM: We tune max_bins in the integer interval [8, 512], min_samples_leaf and max_leaves in the integer interval [1, 50], inner_bags and outer_bags in the integer interval [1, 128], learning_rate in the continuous interval [1e-6, 100] on a log scale, and max_rounds in the integer interval [1000, 10000].

NodeGAM: We tune n_trees in the integer interval [1, 256], n_layers and depth in the integer intervals [1, 4], dropout in the continuous interval [0, 0.9], learning_rate in the continuous interval [1e-3, 1e-2], and weight_decay in the continuous interval [1e-6, 1e-1] on a log scale.

GATSM: We tune nbm_batchnorm in the descret set {False, True}, nbm_dropout in the continuous interval [0, 0.9], attn_emb_size in the integer interval [8, 128], attn_n_heads in the integer interval [1, 8], attn_dropout in the continuous interval [0, 0.9], learning_rate in the continuous interval [1e-3, 1e-2], and weight_decay in the continuous interval [1e-6, 1e-1] on a log scale. The optimal hyper-parameters for GATSM across all experimental datasets are provided in Table 6.

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D Additional experiments

D.1 Inference speed

The inference speed of machine learning models is a crucial metric for real-world systems. We evaluate the throughput of various models. The results are presented in Table 7. Since the datasets have fewer features than the number of basis functions in NBM, NAM achieves higher throughput than NBM. Transparent tabular models typically exhibit fast speeds. However, their throughput significantly decreases in datasets with many features, such as Heartbeat, Mortality, and Sepsis, because they require the same number of feature functions as the number of input features. Transformer shows higher throughput than the transparent time series models because it does not require feature functions, which are the main bottleneck of transparent models. Additionally, the PyTorch implementation of Transformer uses the flash attention mechanism [61] to enhance its efficiency. NATM has slightly higher throughput than GATSM, as it does not require the attention mechanism and has fewer feature functions compared to the number of basis functions in GATSM.

D.2 Number of basis functions

We evaluate GATSM by varying the number of basis functions in the time-sharing NBM. The results for forecasting, binary classification, and multi-class classification datasets are presented in Figure 6. For the Sepsis dataset, using 200 and 300 basis functions causes the out-of-memory error. For the Energy and Heartbeat datasets, performance improves up to 100 basis functions but shows no further benefit when the number of bases exceeds 100. In other datasets, performance changes are not significant with different numbers of basis functions. In addition, there is a trade-off between the number of basis functions and computational speed. Therefore, we recommend generally setting the number of basis functions to 100. Note that the performance of GATSM with this hyper-parameter depends on the dataset size and complexity. Hence, a larger number of basis functions may benefit more complex datasets.

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E Additional visualizations

In addition to the interpretations on the AirQuality dataset in section 5.4, we present another interesting interpretations of GATSM on the Rainfall dataset.

Time-step importance: Figure 7 illustrates the average importance of all time steps at the final time step. The importance exhibit a cyclical pattern of rising and falling at regular intervals, indicating that GATSM effectively captures seasonal patterns in the Rainfall dataset.

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Global feature contribution: Figure 8 illustrates the global behavior of features in the Rainfall dataset, with red bars indicating the density of training samples. Our findings indicate that low Max Temperature and high Min Temperature contribute to an increase in rainfall.

Local time-independent feature contribution: Figure 9 shows the local time-independent feature contributions. Consistent with the global interpretation, Avg. Temperature and Min Temperature have positive correlations with rainfall, while Max Temperature has a negative correlation with rainfall.

Local time-dependent feature contribution: Figure 10 shows the local time-dependent feature 860 contributions. All features exhibit patterns similar to the local time-independent contributions. 861 However, we found that Avg. Temperature and Min Temperature have time lags between feature 862 values and contributions. 863

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Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nGATSM effectively captures temporal patterns and handles dynamic-length time series while preserving transparency, outperforming existing GAMs and matching the performance of black-box models like RNNs and Transformers.\n\nSTRENGTHS:\n* This paper is easy to understand.\n* GATSM can be understood as a linear representation with good transparency.\n* Surprisingly, this method improves performance while providing better interpretability compared with black-box.\n\nWEAKNESSES:\n* It is not clear how multi-head attention works in Definition 3.1 to learn temporal patterns. My understanding is that the global feature interacts with the current feature in Eq.3, so why is it that the input to the attention is not $x$ but the transformed $\\tilde_x$. And then, are temporal patterns captured from attention? \n\n* The addition of attention to NBM is under-motivated, so why not just replace $w^{nbm}$ to attention weight, so that you can learn one less set of parameters $w^{nbm}$.\n\n* The experiment lacks DLinear [1], a strong baseline and providing interpretability. I think it's highly relevant.\n1. Are Transformers Effective for Time Series Forecasting? AAAI 2023.\n\n* Given the emphasis on interpretation or white-box modeling, qualitative experiments of the contributions/explanations need to be compared rather than visualization. If there is no ground-truth of the contribution, occlusion experiments in post-hoc methods [2, 3] can also be designed to explore the trade-off between performance and additive features.\n2. Encoding time-series explanations through self-supervised model behavior consistency, NeurIPS 2023.\n3. TimeX++: learning time-series explanations with information bottleneck, ICML 2024.\n\n* In Table 7, why is the throughput of GATSM so much lower than NBM? Does NBM add up as features at the time level without sharing?\n\nQUESTIONS:\nSee the weaknesses.\n\nLIMITATIONS:\nIt's hard to deal with the higher-order interactions, e.g. GA^2M/GA^NM in time series, since time series often have long time points and the high complexity of gam-based techniques. In addition, the temporal-level causal interrelationships can be further explored.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 2, "DATE": "2024-06-12"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces GATSM(Generalized Additive Time Series Model), designed for handling multivariate time series data with a focus on transparency and interpretability. Using independent networks to learn feature representations and transparent temporal modules to learn cross-time step dynamics, GATSM effectively learns temporal patterns and maintains interpretability.  It achieves comparable results achieves comparable performance to black-box time series models on various datasets, and proves the transparent predictions with cases.\n\nSTRENGTHS:\n1. A key strength of GATSM is its focus on transparency, providing clear insights into the decision-making process, which is crucial for applications in high-stakes domains like healthcare.\n2. The paper presents a thorough evaluation across multiple datasets, including Energy, Rainfall, AirQuality, and several healthcare datasets, showcasing the model's robustness and generalization capabilities.\n3. The authors provide extensive details about the experimental setup, including data splits, hyperparameters, and computational resources, facilitating reproducibility.\n\nWEAKNESSES:\n1.  The need for a large number of feature functions can limit scalability (even if it is reduced from TxM to B), particularly with high-dimensional data.\n2. The dataset tasks encompass both 1-step forecasting and classification, each requiring distinct evaluation metrics. Presenting all results in a single table without proper clarification leads to confusion. \n3. The selected baseline black-box models are relatively simple. Consider including one or two state-of-the-art methods for a more comprehensive comparison.\n\nQUESTIONS:\nCan this model be applied to a multi-step prediction explanation since one-step forecasting is simple to real-world applications.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 2, "DATE": "2024-07-06"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper introduces a Generalized Additive Model for time series, combining feature embedding and attention layer. The proposed solution is evaluated on forecasting, binary and multiclass classification, over 8 datasets, against black box and transparent models. Global, local, time-focused and feature focused interpretability methods are provided.\n\nSTRENGTHS:\nExperimental evaluation is convincing: the presented model has state of the art performance. On the transparency side, the comparison between models allows the author to postulate on the presence of absence of interactions of covariates, and time-specific patterns. Evaluations of weights at the final linear layer give varied visualizations.\n\nThe reasoning behind the model construction and component is clear, and ablation experiment for each component were provided.\n\nPaper is clear with no major problem in writing.\n\nWEAKNESSES:\nI am not sure if the work is original. The idea of using DNN first on the time axis without covariate interaction is not new, but wether there is a model similar to the proposed solution, I do not know. The review of previous works focuses on Generalized Additive Models, but a similar neural structure may have been presented without being positioned as a GAM.\n\nOne improvement to be done would be to add more clarity on figure captions. In its present form, it requires back and forth to the text to understand both what is plotted and what conclusions to draw from it.\n\nQUESTIONS:\nIn forecasting tasks, there are often long horizons to be considered. Is it possible to build a multioutput model for forecasting using GAM formalism? In which case, would the interpretation be able to relate future timestamps together, as series are often autocorrelated?\n\nCan correlation among dimensions be detected with GAM? This would be especially relevant in high dimensional MTS.\n\nLIMITATIONS:\nSeveral limitations are identified: possible overfitting of the model due to overparameterization in NBM part, slow attention mechanisms that do not benefit from state of the art methods, and the fact that it was not evaluated for long sequences (and might not be suited for them).", "TITLE": "Official Review", "RECOMMENDATION": 6, "REVIEWER_CONFIDENCE": 1, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2024-07-12"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis work aims to build transparent models for the time series domain for better interpretability. Specifically, they proposed a work called Generalized Additive Time Series Model (GATSM) that consists of independent feature networks as well as a temporal attention module to learn temporal patterns. The corresponding model can be written into a scalar form to ensure interpretability/transparency. The authors applied their model to several datasets, and showed that GATSM can outperform existing generalized additive models. The model can also be used to interpret the features in original dataset.\n\nSTRENGTHS:\n- Important motivation. Building transparent models for time series is a critical task.\n- The scalar representation of features seems clean (eq 11)\n\nWEAKNESSES:\nWhile this work is not of my direct expertise, I think the following contents have room for improvement:\n\n1. Experimental results are weak.\n- Black-box Time Series Models seem out-of-dated. The authors should consider better models such as TimesNet, PatchTST, FreqTransformer, or Informer for commonly used black-box models.\n- Forecasting tasks use R2 score for evaluation, but an R2 score of 0.07 (or in general, below 0.5) seems very low. The authors should show some visualization examples to ensure the model is functioning.\n- Figure 4/5 are not self-explainable, the authors should try to explain what is happening in those figures, and how the interpretability is quantified.\n- The work could benefit from synthetic dataset, where casual relationships are manually crafted and thus can be evaluated.\n\nQUESTIONS:\n- Line 123: How one should understand the proposed basis functions, are they similar to quantized vectors in works like VQVAE?\n- Eq 5: How would positional embeddings affect the interpretability of the model?\n- How does the interpretability results differ in datasets with very long length (e.g. Mortality) v.s. that of shorter length?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 2, "SOUNDNESS_CORRECTNESS": 2, "DATE": "2024-07-12"}