Compositional Models for Estimating Causal Effects

Purva Pruthi, David Jensen·June 25, 2024

Summary

This paper presents a compositional approach to estimating individual treatment effects (ITE) in structured systems, addressing the limitations of traditional methods that assume homogeneous data and fixed features. The proposed model decomposes units into modular components, estimating potential outcomes at the component level and aggregating them. Key contributions include: 1. A novel compositional framework that generalizes to unseen component combinations and enhances overlap between treatment and control groups. 2. Instance-specific causal models for variable-size units, improving sample efficiency and out-of-distribution generalization. 3. Formalization of the approach, with a focus on additive parallel and hierarchical compositions, and conditions for outperforming non-compositional methods. 4. Evaluation on synthetic and real-world data, showcasing advantages in scenarios with heterogeneous components and computational systems. The study compares compositional models to existing methods, highlights the importance of compositionality in causal inference, and demonstrates its potential in estimating treatment effects in complex systems. Future work will further explore the use of compositional models in machine learning and causal reasoning, addressing broader structured data and understanding their theoretical benefits.

Key findings

2

Paper digest

What problem does the paper attempt to solve? Is this a new problem?

The paper aims to address the challenge of estimating causal effects using compositional models . This problem is not entirely new, as causal effect estimation has been a subject of research in various fields such as econometrics, machine learning, and statistics . The paper contributes to this ongoing research by focusing on the specific approach of using compositional models for estimating causal effects, adding to the existing body of knowledge in this area .


What scientific hypothesis does this paper seek to validate?

This paper aims to validate the scientific hypothesis related to compositional models for estimating causal effects . The focus is on developing and evaluating models that can effectively estimate causal effects in complex systems by leveraging fine-grained information about the system's structure and breaking down causal queries into more detailed queries. The paper explores the benefits of the compositional approach, such as improved sample efficiency, better overlap between treatment and control groups, enhanced out-of-distribution effect estimation, and scalable causal effect estimation for units of variable sizes.


What new ideas, methods, or models does the paper propose? What are the characteristics and advantages compared to previous methods?

The paper "Compositional Models for Estimating Causal Effects" proposes several innovative ideas, methods, and models in the field of causal effect estimation using compositional approaches . Here are some key contributions outlined in the paper:

  1. Compositional Representation for Causal Effect Estimation: The paper introduces a compositional representation of structured units and potential outcomes to estimate individual treatment effects from observational data . This approach involves estimating component-level potential outcomes and aggregating them to estimate unit-level outcomes, providing a fine-grained analysis of individual effect estimation on structured units .

  2. Algorithm for Estimating Individual Treatment Effects (ITE): The paper presents an algorithm to estimate ITE for structured units by considering pre-treatment covariates, binary treatment, potential outcomes, and assumptions of unconfoundedness, overlap, and consistency . The algorithm aims to identify ITE by leveraging observed and unobserved outcomes for each unit based on treatment assignment .

  3. Real-World Evaluation Environments: The paper proposes a set of novel real-world evaluation environments to assess the compositional approach, including query execution in relational databases and matrix processing on different types of computer hardware . These environments are designed to evaluate the performance of the compositional approach compared to existing methods on synthetic and real-world datasets .

  4. Modeling Effects on Compositional Data: The paper implements three compositional models based on the composition type of potential outcomes, independent or joint training of components, and access to fine-grained potential outcomes . These models offer a systematic approach to generalization benefits for effect estimation tasks, especially in high-dimensional observational data settings .

  5. Performance Evaluation: The paper conducts experiments on synthetic data to evaluate the performance of compositional models in different scenarios, such as fixed vs. variable structure of units, composition types, and bias strength variations . The results demonstrate the superiority of compositional models over baselines in terms of effect estimation and sample efficiency, particularly as bias strength increases and in out-of-distribution unit scenarios .

Overall, the paper introduces a comprehensive framework for causal effect estimation using compositional models, offering a novel perspective on reasoning about interventions' effects and making personalized decisions based on structured and compositional data . The compositional approach for estimating causal effects offers several distinct characteristics and advantages compared to previous methods, as detailed in the paper "Compositional Models for Estimating Causal Effects" . Here is an in-depth analysis of these characteristics and advantages with reference to the details in the paper:

  1. Component-Specific Covariates and Treatment: Unlike traditional methods that deal with high-dimensional covariates and treatment for each unit, the compositional approach focuses on lower-dimensional component-specific covariates and treatment, potentially with multiple samples per unit . This characteristic allows for a more fine-grained analysis of individual treatment effects based on structured units, enhancing the precision and granularity of effect estimation compared to unitary approaches .

  2. Modular Architecture for Inference: The compositional approach utilizes a modular architecture to estimate component-level potential outcomes and aggregate them to estimate unit-level outcomes, especially for novel units with unseen component combinations . This modular architecture reflects the interaction structure of components with independent mechanisms, leading to improved estimation of both factual and counterfactual errors and enhancing generalization performance .

  3. Real-World Evaluation Environments: The paper introduces novel real-world evaluation environments to assess the performance of the compositional approach, including query execution in relational databases and matrix processing on various computer hardware setups . By comparing the compositional approach to existing methods on synthetic and real-world datasets, the advantages of the compositional models in terms of accuracy, efficiency, and scalability are demonstrated .

  4. Sample Efficiency and Counterfactual Estimation: The compositional models offer better sample efficiency benefits due to simpler outcome functions at the component level, leading to improved prediction tasks . Moreover, in both experimental and observational data scenarios, the compositional approach excels in estimating counterfactual outcomes by reducing distribution mismatch between control and treated populations, especially in cases of reduced dimensionality at the component level .

  5. Generalization and Out-of-Distribution Performance: Compositional models exhibit systematic generalization benefits, particularly in counterfactual outcome estimation, outperforming baselines on out-of-distribution units and showing robust performance in high-dimensional settings with increasing bias strength .

In summary, the compositional approach stands out for its unique characteristics such as component-specific analysis, modular inference architecture, real-world evaluation environments, sample efficiency, counterfactual estimation capabilities, generalization benefits, and robust performance in diverse data scenarios . These characteristics collectively contribute to the advancement of causal effect estimation methods and offer significant advantages over traditional approaches in structured domains .


Do any related researches exist? Who are the noteworthy researchers on this topic in this field?What is the key to the solution mentioned in the paper?

In the field of causal inference and statistical relational learning, several noteworthy researchers have contributed to related research:

  • N. Friedman, L. Getoor, D. Koller, and A. Pfeffer have worked on learning probabilistic relational models .
  • A. Gelman and J. Hill have focused on data analysis using regression and multilevel/hierarchical models .
  • S. Geman, E. Bienenstock, and R. Doursat have explored neural networks and the bias/variance dilemma .
  • A. M. Gentzel, P. Pruthi, and D. Jensen have discussed the use of experimental data to evaluate methods for observational causal inference .
  • L. Getoor and B. Taskar have introduced statistical relational learning .
  • S. Harada and H. Kashima have worked on estimating individual effects of graph-structured treatments .
  • D. Heckerman and M. P. Wellman have contributed to the field of Bayesian networks .
  • I. Higgins et al. have focused on learning hierarchical compositional visual concepts .
  • J. L. Hill has worked on Bayesian nonparametric modeling for causal inference .
  • P. W. Holland has contributed to statistics and causal inference .
  • D. Hupkes et al. have explored how neural networks generalize in the context of compositionality .

The key to the solution mentioned in the paper may vary depending on the specific research being referenced. Each researcher's work contributes to the broader understanding of causal inference, statistical relational learning, and related topics, offering valuable insights and methodologies for addressing complex problems in these domains.


How were the experiments in the paper designed?

The experiments in the paper were designed as follows:

  • Two types of compositional models were implemented: Additive Parallel Models and Hierarchical Composition Models .
  • For Additive Parallel Models, a three-layer, fully connected MLP architecture was used for neural network models with hidden layer dimension = 64 and ReLU activations. Models were trained using Adam Optimizer with a learning rate of 0.01 .
  • Hierarchical Composition Models utilized a TreeLSTM architecture with a hidden dimension size = 64 and batch size = 32 for each component. Models were trained using Adam optimizer with a learning rate of 0.01. Different training approaches were used for all outcomes of the hierarchical model and the single-outcome model .
  • Baselines such as X-learner and non-parametric double machine learning were implemented using random forests as the base models. The TNet implementation was taken from a specific Github repository .

What is the dataset used for quantitative evaluation? Is the code open source?

The dataset used for quantitative evaluation in the study on compositional models for estimating causal effects consists of real-world data collected from computational systems like databases and computer programs . The code for the compositional models and their evaluation is not explicitly mentioned as open source in the provided context .


Do the experiments and results in the paper provide good support for the scientific hypotheses that need to be verified? Please analyze.

The experiments and results presented in the paper provide substantial support for the scientific hypotheses that need to be verified. The paper extensively explores compositional models for estimating causal effects, focusing on complex, modular systems and decomposing causal queries into finer-grained queries . The experiments include evaluations on synthetic data with variable unit structures, query execution benchmarks, and matrix operation benchmarks . These experiments demonstrate the effectiveness of compositional approaches in improving sample efficiency, enhancing out-of-distribution effect estimation, and enabling scalable causal effect estimation for units of variable sizes .

Moreover, the paper introduces three compositional models based on different composition types of potential outcomes, independent or joint training of components, and access to fine-grained potential outcomes . The models are designed to address the challenges of modeling effects for compositional data and provide insights into the benefits of compositional approaches in causal effect estimation . The experiments conducted on synthetic data and benchmarks showcase the performance of these models, highlighting their ability to handle complex structures and improve causal effect estimation .

Overall, the experiments and results in the paper offer strong empirical evidence supporting the effectiveness and promise of compositional models for estimating causal effects in various scenarios, providing valuable insights into the application of these models in real-world settings .


What are the contributions of this paper?

The paper makes several key contributions:

  • Synthetic Data Experiments: The study evaluates models using synthetic data with variable unit structures and multiple instances of each module, focusing on the additive parallel composition of potential outcomes. The results show the performance of compositional models compared to baselines like TNet and Neural Network, highlighting the impact of unit structure variability on model performance .
  • Model Implementation: Three compositional models are implemented based on different factors such as the composition type of potential outcomes, independent or joint training of components, and access to fine-grained potential outcomes. These models include the additive parallel (all outcomes) model and the hierarchical (all outcomes) model, each with specific characteristics and assumptions .
  • Causal Inference Challenges: The paper addresses challenges in causal effect estimation, particularly in the context of randomized treatments and interventions. It discusses the impact of modified features in query plans due to interventions, emphasizing the need to understand the behavior of query execution engines under interventions for accurate causal effect estimation .

What work can be continued in depth?

Work that can be continued in depth typically involves projects or tasks that require further analysis, research, or development. This could include:

  1. Research projects that require more data collection, analysis, and interpretation.
  2. Complex problem-solving tasks that need further exploration and experimentation.
  3. Creative projects that can be expanded upon with more ideas and iterations.
  4. Skill development activities that require continuous practice and improvement.
  5. Long-term goals that need consistent effort and dedication to achieve.

If you have a specific type of work in mind, feel free to provide more details so I can give you a more tailored response.


Introduction
Background
Limitations of traditional ITE methods
Homogeneity and fixed feature assumptions
Objective
To address these limitations with a novel compositional approach
Method
Compositional Framework
Unseen Component Combinations
Generalizability to novel compositions
Enhancing Overlap
Strategies for improved treatment-control group separation
Instance-Specific Causal Models
Variable-Size Units
Sample efficiency and out-of-distribution performance
Formalization
- Additive Parallel Compositions
- Hierarchical Compositions
Conditions for outperforming non-compositional methods
Model Estimation and Inference
Algorithms and techniques for component-level outcome prediction
Evaluation
Synthetic Data Analysis
Comparisons with existing methods
Assessing performance in heterogeneous scenarios
Real-World Applications
Case studies in computational systems
Demonstrating advantages in complex settings
Theoretical Advantages
Compositionality in causal inference
Potential for machine learning and causal reasoning
Future Directions
Exploration in broader structured data
Theoretical understanding of compositionality benefits
Conclusion
Summary of key contributions
Implications for the field of causal inference and machine learning
Basic info
papers
machine learning
artificial intelligence
methodology
Advanced features
Insights
What is the primary focus of the paper in terms of estimating individual treatment effects?
How does the proposed compositional framework address the limitations of traditional methods for homogeneous data?
What types of real-world data are used to evaluate the effectiveness of the compositional approach in estimating treatment effects?
What are the key contributions of the model, specifically regarding instance-specific causal models and their impact on sample efficiency?

Compositional Models for Estimating Causal Effects

Purva Pruthi, David Jensen·June 25, 2024

Summary

This paper presents a compositional approach to estimating individual treatment effects (ITE) in structured systems, addressing the limitations of traditional methods that assume homogeneous data and fixed features. The proposed model decomposes units into modular components, estimating potential outcomes at the component level and aggregating them. Key contributions include: 1. A novel compositional framework that generalizes to unseen component combinations and enhances overlap between treatment and control groups. 2. Instance-specific causal models for variable-size units, improving sample efficiency and out-of-distribution generalization. 3. Formalization of the approach, with a focus on additive parallel and hierarchical compositions, and conditions for outperforming non-compositional methods. 4. Evaluation on synthetic and real-world data, showcasing advantages in scenarios with heterogeneous components and computational systems. The study compares compositional models to existing methods, highlights the importance of compositionality in causal inference, and demonstrates its potential in estimating treatment effects in complex systems. Future work will further explore the use of compositional models in machine learning and causal reasoning, addressing broader structured data and understanding their theoretical benefits.
Mind map
Conditions for outperforming non-compositional methods
Sample efficiency and out-of-distribution performance
Strategies for improved treatment-control group separation
Generalizability to novel compositions
Demonstrating advantages in complex settings
Case studies in computational systems
Assessing performance in heterogeneous scenarios
Comparisons with existing methods
Algorithms and techniques for component-level outcome prediction
- Hierarchical Compositions
- Additive Parallel Compositions
Formalization
Variable-Size Units
Enhancing Overlap
Unseen Component Combinations
To address these limitations with a novel compositional approach
Homogeneity and fixed feature assumptions
Limitations of traditional ITE methods
Implications for the field of causal inference and machine learning
Summary of key contributions
Theoretical understanding of compositionality benefits
Exploration in broader structured data
Potential for machine learning and causal reasoning
Compositionality in causal inference
Real-World Applications
Synthetic Data Analysis
Model Estimation and Inference
Instance-Specific Causal Models
Compositional Framework
Objective
Background
Conclusion
Future Directions
Theoretical Advantages
Evaluation
Method
Introduction
Outline
Introduction
Background
Limitations of traditional ITE methods
Homogeneity and fixed feature assumptions
Objective
To address these limitations with a novel compositional approach
Method
Compositional Framework
Unseen Component Combinations
Generalizability to novel compositions
Enhancing Overlap
Strategies for improved treatment-control group separation
Instance-Specific Causal Models
Variable-Size Units
Sample efficiency and out-of-distribution performance
Formalization
- Additive Parallel Compositions
- Hierarchical Compositions
Conditions for outperforming non-compositional methods
Model Estimation and Inference
Algorithms and techniques for component-level outcome prediction
Evaluation
Synthetic Data Analysis
Comparisons with existing methods
Assessing performance in heterogeneous scenarios
Real-World Applications
Case studies in computational systems
Demonstrating advantages in complex settings
Theoretical Advantages
Compositionality in causal inference
Potential for machine learning and causal reasoning
Future Directions
Exploration in broader structured data
Theoretical understanding of compositionality benefits
Conclusion
Summary of key contributions
Implications for the field of causal inference and machine learning
Key findings
2

Paper digest

What problem does the paper attempt to solve? Is this a new problem?

The paper aims to address the challenge of estimating causal effects using compositional models . This problem is not entirely new, as causal effect estimation has been a subject of research in various fields such as econometrics, machine learning, and statistics . The paper contributes to this ongoing research by focusing on the specific approach of using compositional models for estimating causal effects, adding to the existing body of knowledge in this area .


What scientific hypothesis does this paper seek to validate?

This paper aims to validate the scientific hypothesis related to compositional models for estimating causal effects . The focus is on developing and evaluating models that can effectively estimate causal effects in complex systems by leveraging fine-grained information about the system's structure and breaking down causal queries into more detailed queries. The paper explores the benefits of the compositional approach, such as improved sample efficiency, better overlap between treatment and control groups, enhanced out-of-distribution effect estimation, and scalable causal effect estimation for units of variable sizes.


What new ideas, methods, or models does the paper propose? What are the characteristics and advantages compared to previous methods?

The paper "Compositional Models for Estimating Causal Effects" proposes several innovative ideas, methods, and models in the field of causal effect estimation using compositional approaches . Here are some key contributions outlined in the paper:

  1. Compositional Representation for Causal Effect Estimation: The paper introduces a compositional representation of structured units and potential outcomes to estimate individual treatment effects from observational data . This approach involves estimating component-level potential outcomes and aggregating them to estimate unit-level outcomes, providing a fine-grained analysis of individual effect estimation on structured units .

  2. Algorithm for Estimating Individual Treatment Effects (ITE): The paper presents an algorithm to estimate ITE for structured units by considering pre-treatment covariates, binary treatment, potential outcomes, and assumptions of unconfoundedness, overlap, and consistency . The algorithm aims to identify ITE by leveraging observed and unobserved outcomes for each unit based on treatment assignment .

  3. Real-World Evaluation Environments: The paper proposes a set of novel real-world evaluation environments to assess the compositional approach, including query execution in relational databases and matrix processing on different types of computer hardware . These environments are designed to evaluate the performance of the compositional approach compared to existing methods on synthetic and real-world datasets .

  4. Modeling Effects on Compositional Data: The paper implements three compositional models based on the composition type of potential outcomes, independent or joint training of components, and access to fine-grained potential outcomes . These models offer a systematic approach to generalization benefits for effect estimation tasks, especially in high-dimensional observational data settings .

  5. Performance Evaluation: The paper conducts experiments on synthetic data to evaluate the performance of compositional models in different scenarios, such as fixed vs. variable structure of units, composition types, and bias strength variations . The results demonstrate the superiority of compositional models over baselines in terms of effect estimation and sample efficiency, particularly as bias strength increases and in out-of-distribution unit scenarios .

Overall, the paper introduces a comprehensive framework for causal effect estimation using compositional models, offering a novel perspective on reasoning about interventions' effects and making personalized decisions based on structured and compositional data . The compositional approach for estimating causal effects offers several distinct characteristics and advantages compared to previous methods, as detailed in the paper "Compositional Models for Estimating Causal Effects" . Here is an in-depth analysis of these characteristics and advantages with reference to the details in the paper:

  1. Component-Specific Covariates and Treatment: Unlike traditional methods that deal with high-dimensional covariates and treatment for each unit, the compositional approach focuses on lower-dimensional component-specific covariates and treatment, potentially with multiple samples per unit . This characteristic allows for a more fine-grained analysis of individual treatment effects based on structured units, enhancing the precision and granularity of effect estimation compared to unitary approaches .

  2. Modular Architecture for Inference: The compositional approach utilizes a modular architecture to estimate component-level potential outcomes and aggregate them to estimate unit-level outcomes, especially for novel units with unseen component combinations . This modular architecture reflects the interaction structure of components with independent mechanisms, leading to improved estimation of both factual and counterfactual errors and enhancing generalization performance .

  3. Real-World Evaluation Environments: The paper introduces novel real-world evaluation environments to assess the performance of the compositional approach, including query execution in relational databases and matrix processing on various computer hardware setups . By comparing the compositional approach to existing methods on synthetic and real-world datasets, the advantages of the compositional models in terms of accuracy, efficiency, and scalability are demonstrated .

  4. Sample Efficiency and Counterfactual Estimation: The compositional models offer better sample efficiency benefits due to simpler outcome functions at the component level, leading to improved prediction tasks . Moreover, in both experimental and observational data scenarios, the compositional approach excels in estimating counterfactual outcomes by reducing distribution mismatch between control and treated populations, especially in cases of reduced dimensionality at the component level .

  5. Generalization and Out-of-Distribution Performance: Compositional models exhibit systematic generalization benefits, particularly in counterfactual outcome estimation, outperforming baselines on out-of-distribution units and showing robust performance in high-dimensional settings with increasing bias strength .

In summary, the compositional approach stands out for its unique characteristics such as component-specific analysis, modular inference architecture, real-world evaluation environments, sample efficiency, counterfactual estimation capabilities, generalization benefits, and robust performance in diverse data scenarios . These characteristics collectively contribute to the advancement of causal effect estimation methods and offer significant advantages over traditional approaches in structured domains .


Do any related researches exist? Who are the noteworthy researchers on this topic in this field?What is the key to the solution mentioned in the paper?

In the field of causal inference and statistical relational learning, several noteworthy researchers have contributed to related research:

  • N. Friedman, L. Getoor, D. Koller, and A. Pfeffer have worked on learning probabilistic relational models .
  • A. Gelman and J. Hill have focused on data analysis using regression and multilevel/hierarchical models .
  • S. Geman, E. Bienenstock, and R. Doursat have explored neural networks and the bias/variance dilemma .
  • A. M. Gentzel, P. Pruthi, and D. Jensen have discussed the use of experimental data to evaluate methods for observational causal inference .
  • L. Getoor and B. Taskar have introduced statistical relational learning .
  • S. Harada and H. Kashima have worked on estimating individual effects of graph-structured treatments .
  • D. Heckerman and M. P. Wellman have contributed to the field of Bayesian networks .
  • I. Higgins et al. have focused on learning hierarchical compositional visual concepts .
  • J. L. Hill has worked on Bayesian nonparametric modeling for causal inference .
  • P. W. Holland has contributed to statistics and causal inference .
  • D. Hupkes et al. have explored how neural networks generalize in the context of compositionality .

The key to the solution mentioned in the paper may vary depending on the specific research being referenced. Each researcher's work contributes to the broader understanding of causal inference, statistical relational learning, and related topics, offering valuable insights and methodologies for addressing complex problems in these domains.


How were the experiments in the paper designed?

The experiments in the paper were designed as follows:

  • Two types of compositional models were implemented: Additive Parallel Models and Hierarchical Composition Models .
  • For Additive Parallel Models, a three-layer, fully connected MLP architecture was used for neural network models with hidden layer dimension = 64 and ReLU activations. Models were trained using Adam Optimizer with a learning rate of 0.01 .
  • Hierarchical Composition Models utilized a TreeLSTM architecture with a hidden dimension size = 64 and batch size = 32 for each component. Models were trained using Adam optimizer with a learning rate of 0.01. Different training approaches were used for all outcomes of the hierarchical model and the single-outcome model .
  • Baselines such as X-learner and non-parametric double machine learning were implemented using random forests as the base models. The TNet implementation was taken from a specific Github repository .

What is the dataset used for quantitative evaluation? Is the code open source?

The dataset used for quantitative evaluation in the study on compositional models for estimating causal effects consists of real-world data collected from computational systems like databases and computer programs . The code for the compositional models and their evaluation is not explicitly mentioned as open source in the provided context .


Do the experiments and results in the paper provide good support for the scientific hypotheses that need to be verified? Please analyze.

The experiments and results presented in the paper provide substantial support for the scientific hypotheses that need to be verified. The paper extensively explores compositional models for estimating causal effects, focusing on complex, modular systems and decomposing causal queries into finer-grained queries . The experiments include evaluations on synthetic data with variable unit structures, query execution benchmarks, and matrix operation benchmarks . These experiments demonstrate the effectiveness of compositional approaches in improving sample efficiency, enhancing out-of-distribution effect estimation, and enabling scalable causal effect estimation for units of variable sizes .

Moreover, the paper introduces three compositional models based on different composition types of potential outcomes, independent or joint training of components, and access to fine-grained potential outcomes . The models are designed to address the challenges of modeling effects for compositional data and provide insights into the benefits of compositional approaches in causal effect estimation . The experiments conducted on synthetic data and benchmarks showcase the performance of these models, highlighting their ability to handle complex structures and improve causal effect estimation .

Overall, the experiments and results in the paper offer strong empirical evidence supporting the effectiveness and promise of compositional models for estimating causal effects in various scenarios, providing valuable insights into the application of these models in real-world settings .


What are the contributions of this paper?

The paper makes several key contributions:

  • Synthetic Data Experiments: The study evaluates models using synthetic data with variable unit structures and multiple instances of each module, focusing on the additive parallel composition of potential outcomes. The results show the performance of compositional models compared to baselines like TNet and Neural Network, highlighting the impact of unit structure variability on model performance .
  • Model Implementation: Three compositional models are implemented based on different factors such as the composition type of potential outcomes, independent or joint training of components, and access to fine-grained potential outcomes. These models include the additive parallel (all outcomes) model and the hierarchical (all outcomes) model, each with specific characteristics and assumptions .
  • Causal Inference Challenges: The paper addresses challenges in causal effect estimation, particularly in the context of randomized treatments and interventions. It discusses the impact of modified features in query plans due to interventions, emphasizing the need to understand the behavior of query execution engines under interventions for accurate causal effect estimation .

What work can be continued in depth?

Work that can be continued in depth typically involves projects or tasks that require further analysis, research, or development. This could include:

  1. Research projects that require more data collection, analysis, and interpretation.
  2. Complex problem-solving tasks that need further exploration and experimentation.
  3. Creative projects that can be expanded upon with more ideas and iterations.
  4. Skill development activities that require continuous practice and improvement.
  5. Long-term goals that need consistent effort and dedication to achieve.

If you have a specific type of work in mind, feel free to provide more details so I can give you a more tailored response.

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