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How can decision-makers effectively learn from sequential sampling when statistical models are misspecified?

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This video discusses the importance of algorithms and their reliance on accurately specified models. It emphasizes that the closer a model reflects reality, the better the algorithm's performance will be. However, when models are mis-specified, which is a common issue, the algorithms may fail to deliver expected results.

The key challenges highlighted include:

1. **Model Enrichment:** The need to enhance models, which can be overly simplistic. For instance, in complex scenarios like pharmaceutical trials, oversimplification could lead to unreliable results due to overlooking crucial patient and environmental factors.

2. **Acknowledging Model Mis-specification:** There’s a tendency among practitioners to overtrust their models despite the common statistical adage that “all models are wrong, but some are useful.” Ignoring mis-specification can yield inefficient results, especially in sequential learning where early poor decisions may compound over time.

The discussion introduces the concept of feature-based modeling, which simplifies complex decision-making processes (like product testing) by focusing on relevant features rather than testing every possible combination.

This video also presents the “prospective sampling principle,” a method for addressing mis-specification by predicting how biases might change with new sample allocations. This video principle ensures that even in mis-specified environments, sampling strategies can result in better decisions.

Finally, the text points out that mis-specification impacts numerous sequential learning scenarios across various applications, urging both academics and practitioners to be cautious about model accuracy. The research aims to pave the way for future studies addressing these challenges.

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Here are five key points from the video:

1. **Importance of Model Accuracy**: The performance of algorithms is heavily dependent on the model used to create them, and the closer the model reflects reality, the better the algorithm performs. Mis-specified models can lead to poor algorithm outcomes.

2. **Challenges in Model Specification**: The primary challenges in the modeling stage involve enhancing the model to accurately capture complexities of real-world situations, while avoiding oversimplification that can render the model unreliable.

3. **Consequences of Model Mis-specification**: Mis-specifications can lead to biased estimates, particularly in sequential learning scenarios. Such biases can create a vicious cycle where poor estimates lead to suboptimal decisions, continuously compounding the errors throughout the decision-making process.

4. **Feature-Based Modeling Benefits**: Using a feature-based approach can greatly simplify complex modeling tasks. By estimating a smaller number of parameters rather than trying to account for all combinations of features, modeling becomes more manageable and efficient.

5. **Evolution of Bias in Sampling Strategies**: The video introduces a prospective sampling principle that accounts for how parameter bias may evolve with new sample allocations. This principle can improve decision-making in mis-specified models and offers a cautionary note on the limitations of traditional myopic sampling strategies in real-world applications.

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Here are some key quotes extracted from the video, along with their convideos:

1. **"The closer the model reflects the reality, the better the algorithm will perform in practice."**
- This emphasizes the importance of model accuracy in improving algorithm performance.

2. **"Model mis-specification refers to the situation that the model you're using is not perfectly reflecting the reality."**
- This introduces the concept of model mis-specification and indicates its potential problems in application.

3. **"In statistics, there is a well-known saying that all models are wrong, but some are useful."**
- Acknowledges that while no model can completely capture reality, some can still be practical and beneficial.

4. **"Even a minimum level of mis-specification can lead to significant inefficiencies in sequential learning."**
- Highlights how even small inaccuracies in a model can propagate through learning processes, causing major issues.

5. **"In sequential learning problems, the impact of model mis-specification can become bigger and bigger throughout the process."**
- Indicates that the effects of mis-specification can compound over time, worsening decision-making.

6. **"Although we have a small number of features, the number of combinations can exceed 6,000."**
- Points out the complexity of modeling when multiple features are involved, stressing the implementation difficulties in practical scenarios.

7. **"Sample selection endogeneity refers to the situation in which this bias is influenced by how you allocate samples across systems during the experiments."**
- Defines a specific type of bias that can arise in the sampling process due to mis-specification.

8. **"Our research demonstrates that we can predict how the bias will change with the new sample allocation."**
- Discusses the capability developed in their research to adapt to changing models and maintain accurate decision-making.

9. **"Accumulate more samples can actually increase your confidence in a wrong decision."**
- Challenges the common belief that more data automatically leads to better decisions, warning against misinterpretations.

10. **"The primary reason for this inefficiency is that mis-specified models lead to biased estimates, and this negative effect becomes amplified as we go in the sequential learning process."**
- Summarizes the core issue of their findings, linking model quality directly to decision-making efficacy.

These quotes distill the main ideas and arguments present in the video regarding the challenges and implications of model specification in algorithmic decision-making, particularly in the convideo of sequential learning.

X-TIMESTAMP-MAP=LOCAL:00:00:00.000,MPEGTS:90000

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Many situations we use, use algorithms,

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and all of the algorithms are based on a model, okay?

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And the closer the model reflects the reality,

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the better the algorithm will perform in practice, right?

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The model is specification refers to the situation

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that the model you're using

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is not perfectly reflecting the reality, and

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therefore the algorithm that you want

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to use may not really perform well as expected in practice.

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So that's the situation that we want to address

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in the paper that we study.

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The main challenges are associated with the model.

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So I wanna emphasize a few key challenges

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in the modeling stage of the process.

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Well, the first major challenge is of course,

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to enhance the model as much as possible.

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A not even simple model is good

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because it facilitates a attractive

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and implementable processes for top rank selection.

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However, such a model may be too simplistic

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to accurately reflect reality, as I mentioned earlier.

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And consequently,

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top ranked selection could become significantly unreliable.

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For example, think about pharmaceutical products

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used in clinical trials.

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These products involve very complex chemical compounds,

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and their effectiveness often depends on,

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many different ca patient characteristics such as gender,

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age, medical history.

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It may also depends on many environmental factors

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that may not be directly observable in the data.

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Data scientists

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or decision makers may lack expertise in chemistry

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and might just try to approximate this effectiveness

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using just a simple model based on

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a few observable variables.

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And this may not work well in practice.

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So to build a more reliable model, they need

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to consult with professionals.

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Um, so I would say enriching the model as much

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as possible is the first challenge.

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But once a model is established,

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the next major challenge is to acknowledge the possibility

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of model mis specification.

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And this is interesting to say, while,

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because this may seem quite, obvious,

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but this is actually a common mistake

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that happens in practice.

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Well, in statistics, there is a well known age saying

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that all models are wrong, but some are useful.

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Well, this statement highlights that mathematical models,

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even if they are enriched to a certain extent,

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cannot fully capture the complexity

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of the reality in business context.

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Uh, data scientists

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or decision makers often, tend

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to overtrust their models,

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Partly because they wish to demonstrate

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that their decisions are supported by vigorous

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and accurate mathematical framework.

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But in top rank selection problem,

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ignoring modern specification,

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can have detrimental impact

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because, such a problem involves sequential learning.

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Specifically, our research indicates

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that even a minimum level of mis specification

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can lead to a,

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a significant inefficiencies in sequential learning.

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More specifically, a mis specification can result in biased

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estimates leading you

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to make a poor decision at a certain stage of the procedure.

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And then what happens is that in subsequent stages,

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this poor decision can make your estimate even more biased,

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making your decision even worse.

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And, and this, this,

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vicious cycle can go on and on and on.

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In other words, in sequential learning problems, the impact

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of modern specification can become bigger

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and bigger throughout the process,

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ultimately increasing the likelihood

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of selecting a really, really poor system.

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So this is exactly the challenge we tackle in our research

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to illustrate the

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how feature-based modeling enhances

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this sampling efficiency.

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Uh, let me give you an example. Okay?

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So consider this example of, manufacturer

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trying to design a fashion item, okay?

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But each item may be defined, by a combination

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of features such as the size, color, material,

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fit pattern, and price of the product, right?

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So while the manufacturer may not know which version

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of the product will be most profitable, they can do,

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a kind of product testing

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or online service to measure consumer preferences.

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Specifically, they can show different versions of product

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to different customers

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and record their responses to eventually

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identify the most profitable version of the product.

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But however, in this stage,

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they face a significant challenge already.

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So each version of the product is characterized by, well,

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six different features, right?

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As I mentioned earlier. So

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although we have a small number of features, the number

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of combinations can exceed 6,000.

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And of course, given a limited number of customers testing,

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6,000 version

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of the product individually become nearly impossible.

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But feature-based approach significantly

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simplifies this problem because instead

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of testing 6,000 individual versions of the product,

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you only need to estimate six parameters

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making this estimation task much more manageable.

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So I would say this is the most important benefit

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of feature-based modeling.

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Let me first clarify what we mean

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by simple selection endogeneity.

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Well, in general, when the model is Mrs.

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Mis specified, the estimated parameters can be biased.

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This is a well known fact in statistics.

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And, and this situation is commonly referred to

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as indigeneity.

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Uh, sample selection indigeneity refers to the

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situation in which this bias is influenced by

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how you allocate samples across systems

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during the experiments.

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For example, suppose

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that you have a bias estimate at a certain point

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of the process, and then based on that, your optimizer

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will tell you that, you have

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to allocate more samples to product one.

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You follow that suggestion, you allocate more samples

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of product one, but now the sample allocation is changed,

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and the sample selection in those 80 tells you

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that the prior estimates

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of the parameter is no longer valid.

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You will obtain a new estimate of the parameter,

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which could be significantly different than

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the prior estimate.

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In other words, the earlier decision based on the prior

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estimate is no longer optimal.

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At the current time point, the situation is akin

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to chasing a moving target.

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As you take a step towards it,

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the target itself is shifting in a different direction,

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making your previous movement suboptimal.

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So in our paper, we introduced this prospective sampling

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principle to address the issue.

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Uh, this could be a little bit technical,

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but let me try to be simple.

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So, so, we know

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that the estimates will always be biased under a

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mis mis specified model.

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However, our research demonstrates that, we can predict

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how the bias will change with the new sample allocation.

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So this capability can make a lot of things different

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In traditional sampling strategies,

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optimal allocation is determined solely by sampling history.

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However, in our respective sampling strategies,

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we calculate optimal allocation using this prospective

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estimator instead of the plain estimator

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that you probably have learned in statistics 1 0 1,

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this prospective estimator incorporates how biases

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may evolve in the future, and

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therefore the sampling decision based on this estimator will

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remain optimal in the future.

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So this is, roughly the idea behind it,

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behind the sample, prospective sampling.

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In recent, recent decades, probably from, the year

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of 1980s, myopic sampling strategies

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have been developed

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and examined in academics from different perspectives.

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And these strategies,

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myopic strategies have consistently demonstrated

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strong performance in extensive simulation studies.

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But these simulations,

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however, typically generate data based on a

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well specified model.

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So it's not surprising

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that myopic strategists excel in such

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controlled environments.

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Alright, however, even the most advanced myopic strategists

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may struggle in reality

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because models in reality are often mis, mis specified,

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to a different degrees.

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If the mis the level of mis specification is substantial,

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then accumulating more samples

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can actually increase your confidence in a wrong decision.

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This contradicts the common belief

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that the larger the data set, the better the inference, and

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therefore the better the decisions.

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Well, our findings reveal that

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more data can in fact worsen, decision making.

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Well, the prospective principle we propose in the paper

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ensures that myopic strategies

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can remain effective even in this mis

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specified environments.

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With our principle, as we gather more data, we guarantee

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that we make better decisions,

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ultimately increasing the chance

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of selecting top ranked systems.

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Importantly, this principle is very genital

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and can be applied to

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virtually all myopic strategies developed

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in the, in the past.

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So for example, if you provide any version

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of myop myopic policy to me, then I can easily adapt it

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to make it perform well in the real world

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mis specified settings.

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Using our prospective principle, we focus on the problem

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of selecting top rank system.

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And this problem is just a subset of, of broader area

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of sequential learning problems,

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which is gaining increasing attention in the AI

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and machine learning communities.

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Um, well, as mentioned earlier, we have discovered

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that even the most sophisticated,

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myopic strategies can falter in real world scenarios

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where models are frequently mis specified.

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The primary reason for this inefficiency, again, is

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that mis, mis specified models lead to biased estimate,

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and this negative effects becomes amplified

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as we go in the sequential learning process.

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And here I would like to emphasize

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that this negative IM impact

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is not really unique in the problem that we study,

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but actually this is common problem across many dyna,

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many sequential learning problems,

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including the celebrated multi-arm banded problems

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and their variations.

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And these problems have a very wide range

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of applications in business operations,

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including dynamic pricing in

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and revenue management, healthcare operations,

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clinical trials, recommendation systems on digital

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platforms and et cetera.

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So although our work does not offer specific solutions

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to each of these broader issues,

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our work serves as a cautionary note that bo note

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for both academics

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and practitioners regarding the potential risk

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of modern specification in sequential learning problems.

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So I believe that, I believe

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and hope that our research opens a promising avenue

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for future research in this broader field of study.

Challenges in Algorithmic Model Specification

00:00:00 - Many situations we use, use algorithms, and all of the algorithms are based on a model, okay? And the closer the model reflects the reality, the better the algorithm will perform in practice, right? The model is specification refers to the situation that the model you're using is not perfectly reflecting the reality, and therefore the algorithm that you want to use may not really perform well as expected in practice.

00:00:33 - in the paper that we study. The main challenges are associated with the model. So I wanna emphasize a few key challenges in the modeling stage of the process. Well, the first major challenge is of course, to enhance the model as much as possible. A not even simple model is good because it facilitates a attractive and implementable processes for top rank selection. However, such a model may be too simplistic

00:01:07 - And consequently, top ranked selection could become significantly unreliable. For example, think about pharmaceutical products used in clinical trials. These products involve very complex chemical compounds, and their effectiveness often depends on, many different ca patient characteristics such as gender, age, medical history. It may also depends on many environmental factors

Challenges in Model Accuracy and Reliance in Data Science

00:01:41 - Data scientists or decision makers may lack expertise in chemistry and might just try to approximate this effectiveness using just a simple model based on a few observable variables. And this may not work well in practice. So to build a more reliable model, they need to consult with professionals. so I would say enriching the model as much

00:02:10 - But once a model is established, the next major challenge is to acknowledge the possibility of model mis specification. And this is interesting to say, while, because this may seem quite, obvious, but this is actually a common mistake that happens in practice. Well, in statistics, there is a well known age saying that all models are wrong, but some are useful.

00:02:42 - even if they are enriched to a certain extent, cannot fully capture the complexity of the reality in business context. data scientists or decision makers often, tend to overtrust their models, Partly because they wish to demonstrate that their decisions are supported by vigorous and accurate mathematical framework. But in top rank selection problem,

Impact of Model Mis-specification in Sequential Learning

00:03:14 - can have detrimental impact because, such a problem involves sequential learning. Specifically, our research indicates that even a minimum level of mis specification can lead to a, a significant inefficiencies in sequential learning. More specifically, a mis specification can result in biased estimates leading you to make a poor decision at a certain stage of the procedure.

00:03:51 - this poor decision can make your estimate even more biased, making your decision even worse. And, and this, this, vicious cycle can go on and on and on. In other words, in sequential learning problems, the impact of modern specification can become bigger and bigger throughout the process, ultimately increasing the likelihood of selecting a really, really poor system.

00:04:22 - to illustrate the how feature-based modeling enhances this sampling efficiency. let me give you an example. Okay? So consider this example of, manufacturer trying to design a fashion item, okay? But each item may be defined, by a combination of features such as the size, color, material, fit pattern, and price of the product, right?

Optimizing Product Design Through Feature-Based Modeling

00:04:53 - of the product will be most profitable, they can do, a kind of product testing or online service to measure consumer preferences. Specifically, they can show different versions of product to different customers and record their responses to eventually identify the most profitable version of the product. But however, in this stage, they face a significant challenge already.

00:05:25 - six different features, right? As I mentioned earlier. So although we have a small number of features, the number of combinations can exceed 6,000. And of course, given a limited number of customers testing, 6,000 version of the product individually become nearly impossible. But feature-based approach significantly simplifies this problem because instead

00:05:57 - you only need to estimate six parameters making this estimation task much more manageable. So I would say this is the most important benefit of feature-based modeling. Let me first clarify what we mean by simple selection endogeneity. Well, in general, when the model is Mrs. Mis specified, the estimated parameters can be biased. This is a well known fact in statistics.

Challenges of Sample Selection Indigeneity in Experimental Design

00:06:25 - as indigeneity. sample selection indigeneity refers to the situation in which this bias is influenced by how you allocate samples across systems during the experiments. For example, suppose that you have a bias estimate at a certain point of the process, and then based on that, your optimizer will tell you that, you have to allocate more samples to product one.

00:06:57 - of product one, but now the sample allocation is changed, and the sample selection in those 80 tells you that the prior estimates of the parameter is no longer valid. You will obtain a new estimate of the parameter, which could be significantly different than the prior estimate. In other words, the earlier decision based on the prior

00:07:27 - At the current time point, the situation is akin to chasing a moving target. As you take a step towards it, the target itself is shifting in a different direction, making your previous movement suboptimal. So in our paper, we introduced this prospective sampling principle to address the issue. this could be a little bit technical, but let me try to be simple.

Optimizing Sampling Through Predictive Bias Management

00:07:58 - that the estimates will always be biased under a mis mis specified model. However, our research demonstrates that, we can predict how the bias will change with the new sample allocation. So this capability can make a lot of things different In traditional sampling strategies, optimal allocation is determined solely by sampling history.

00:08:31 - we calculate optimal allocation using this prospective estimator instead of the plain estimator that you probably have learned in statistics 1 0 1, this prospective estimator incorporates how biases may evolve in the future, and therefore the sampling decision based on this estimator will remain optimal in the future.

00:09:01 - behind the sample, prospective sampling. In recent, recent decades, probably from, the year of 1980s, myopic sampling strategies have been developed and examined in academics from different perspectives. And these strategies, myopic strategies have consistently demonstrated strong performance in extensive simulation studies.

Challenges of Myopic Strategies in Mis-Specified Models

00:09:31 - however, typically generate data based on a well specified model. So it's not surprising that myopic strategists excel in such controlled environments. Alright, however, even the most advanced myopic strategists may struggle in reality because models in reality are often mis, mis specified, to a different degrees.

00:10:02 - then accumulating more samples can actually increase your confidence in a wrong decision. This contradicts the common belief that the larger the data set, the better the inference, and therefore the better the decisions. Well, our findings reveal that more data can in fact worsen, decision making. Well, the prospective principle we propose in the paper

00:10:32 - can remain effective even in this mis specified environments. With our principle, as we gather more data, we guarantee that we make better decisions, ultimately increasing the chance of selecting top ranked systems. Importantly, this principle is very genital and can be applied to virtually all myopic strategies developed in the, in the past.

Challenges of Myopic Strategies in Sequential Learning

00:11:02 - of myop myopic policy to me, then I can easily adapt it to make it perform well in the real world mis specified settings. Using our prospective principle, we focus on the problem of selecting top rank system. And this problem is just a subset of, of broader area of sequential learning problems, which is gaining increasing attention in the AI and machine learning communities.

00:11:36 - that even the most sophisticated, myopic strategies can falter in real world scenarios where models are frequently mis specified. The primary reason for this inefficiency, again, is that mis, mis specified models lead to biased estimate, and this negative effects becomes amplified as we go in the sequential learning process.

00:12:05 - that this negative IM impact is not really unique in the problem that we study, but actually this is common problem across many dyna, many sequential learning problems, including the celebrated multi-arm banded problems and their variations. And these problems have a very wide range of applications in business operations, including dynamic pricing in and revenue management, healthcare operations,

Cautionary Insights on Model Mis-specification in Sequential Learning

00:12:40 - platforms and et cetera. So although our work does not offer specific solutions to each of these broader issues, our work serves as a cautionary note that bo note for both academics and practitioners regarding the potential risk of modern specification in sequential learning problems. So I believe that, I believe and hope that our research opens a promising avenue

00:13:09 -

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