5 ms·

I don’t agree with this. For example, you can set up a collection of assumptions to underpin frequentist statistics, and then create a set of theorems about con

by mlthoughts2018 8y ago

I don’t agree with this. For example, you can set up a collection of assumptions to underpin frequentist statistics, and then create a set of theorems about consistent or unbiased estimators, and develop a theory like that of p-values. But then in a practical setting, the model doesn’t correspond to something physical or to the inference goal of a practitioner. The p-value tells you something about the relative extremity of a certain statistic that, under certain assumptions, will have a particular distribution. The practitioner wants to know the posterior probability of a particular model or hypothesis given the data, and the frequentist outcome literally can’t comment on it. In this sense I think being able to state assumptions and connect them to outcomes with theorems is good, but not always necessary or even sufficient for applied work. And there can creep in nasty subjective aspects of the problem that are uniquely defined by the specific inference goals at hand. Proofs about how a model would behave under assumptions are often totally useless in these cases. Practitioners don’t use linear regression for complex financial models because the assumptions hold or because of nice properties if the assumptions held. They use them because it’s simple and easy and sort of “just works” despite glaring flaws.

cosmic_ape 8y ago
I don't think there's a contradiction. My comment was about what it means to understand the model, or perhaps about what it means to do science, but not about what is necessary or sufficient for applied work. But if we do talk about that though. Yes, science proceeds by modifying or sometimes totally abandoning the assumptions. No silver bullet, and the point is to assume as little as possible. In general, if things "just work", its not a reason to abandon attempts to understand them. Things "just work" until they don't, especially in finance. Consider two guys. Guy A, he predicts that the sun rises every day and is there until dusk. It "works", and so, as the joke goes, he does not touch anything. And guy B, he knows physics and has telescopes. And he can predict the solar eclipses. He knows the failure modes of the model of guy A. Consider the difference between the two.
- mlthoughts2018 8y ago
  I feel like you’re arguing against yourself here. Guy A’s shallow model would easily be considered more interpretable than Guy B’s sophisticated astronomical physics model, though Guy B’s model is clearly able to articulate more detailed predictions about what might happen. Guy B’s model is less interpretable, but because it “just works” in a vastly greater number of ways (can be applied to the moon, constellations, other planets), people use it or care about it. If all that astronomy offered was a more verbose description of why the sun rises, yielding literally zero different predictions from Guy A’s super simple model, no one would care, and might call Guy B a witch! I’d argue that what matters for science is pure predictive efficacy. That’s it. If you can explain something, it means you can accurately predict something about an unknown state of affairs that would falsify your model if your prediction is wrong. That’s it. Any other kind of explainability is just a matter of linguistic convenience. Of course there is overfitting, etc., but that’s just part of refining the model to yield greater predictive accuracy on unseen data (less generalization error). It’s still all about putting your predictions where your mouth is. If the differing theories of Guy A and Guy B cannot be separated by actually testing the predictions they make, then there is no “interpretability” — just linguistic hand waving. Incidentally I think a lot of modern focus on interpretability is actually about how to be a political gatekeeper or taste-maker through linguistic hand waving, and is not about developing models who better survive the rigors of being required to make real predictions about states of affairs.
romaniv 8y ago
>But then in a practical setting, the model doesn’t correspond to something physical or to the inference goal of a practitioner. How does this invalidate the notion of interpretability? A model can be both wrong/misapplied and fully interpretable.
- mlthoughts2018 8y ago
  > “How does this invalidate the notion of interpretability?” Who said that it did? I’m saying the development of a model that yields scientific progress doesn’t have to have a connection to the parent comment’s proposed definition of interpretability, and may have competing interpretability concerns driven by specific inference goals that have nothing to do with proofs about the model under assumptions.
  - romaniv 8y ago
    >I’m saying the development of a model that yields scientific progress doesn’t have to have a connection to the parent comment’s proposed definition of interpretability Let's say someone used a neural network to predict planetary positions as a function of time, mass and so on. They made a network with several hundred parameters, trained until it stopped converging and published their final state vector. Would that ever lead to gravitational theory?
    - mlthoughts2018 8y ago
      What do you mean by “gravitational theory” apart from “correctly accounts for predicting the gravitational effects that we observe”? If a neural net can do that, then yes, a perfectly “elegant” theory could be the giant enumeration of a big ugly bunch of parameters. Of course we might suspect that’s overfitting and whittle down to a compact description, and that’s great, but doesn’t make the ugly enumeration of a big model any less scientific. Another point of view would be to say how does the Wiles proof of Fermat’s Last Theorem give us “understanding” (or substitute virtually any non-constructive existence proof, or proofs by contradiction, such as for the Halting Problem). Compact math descriptions are good, don’t get me wrong. When the mechanism of some data generating process is actually oriented in such a way that we can get a concise math description then we absolutely should. But that is largely unrelated to advancing understanding or scientific progress, which can perfectly be some ugly enumerated garble of parameters, or some extremely piecewise solution space. Not every data generating process is required to admit a concise mathematical description.

cosmic_ape 8y ago

I don't think there's a contradiction. My comment was about what it means to understand the model, or perhaps about what it means to do science, but not about what is necessary or sufficient for applied work. But if we do talk about that though. Yes, science proceeds by modifying or sometimes totally abandoning the assumptions. No silver bullet, and the point is to assume as little as possible. In general, if things "just work", its not a reason to abandon attempts to understand them. Things "just work" until they don't, especially in finance. Consider two guys. Guy A, he predicts that the sun rises every day and is there until dusk. It "works", and so, as the joke goes, he does not touch anything. And guy B, he knows physics and has telescopes. And he can predict the solar eclipses. He knows the failure modes of the model of guy A. Consider the difference between the two.

mlthoughts2018 8y ago
I feel like you’re arguing against yourself here. Guy A’s shallow model would easily be considered more interpretable than Guy B’s sophisticated astronomical physics model, though Guy B’s model is clearly able to articulate more detailed predictions about what might happen. Guy B’s model is less interpretable, but because it “just works” in a vastly greater number of ways (can be applied to the moon, constellations, other planets), people use it or care about it. If all that astronomy offered was a more verbose description of why the sun rises, yielding literally zero different predictions from Guy A’s super simple model, no one would care, and might call Guy B a witch! I’d argue that what matters for science is pure predictive efficacy. That’s it. If you can explain something, it means you can accurately predict something about an unknown state of affairs that would falsify your model if your prediction is wrong. That’s it. Any other kind of explainability is just a matter of linguistic convenience. Of course there is overfitting, etc., but that’s just part of refining the model to yield greater predictive accuracy on unseen data (less generalization error). It’s still all about putting your predictions where your mouth is. If the differing theories of Guy A and Guy B cannot be separated by actually testing the predictions they make, then there is no “interpretability” — just linguistic hand waving. Incidentally I think a lot of modern focus on interpretability is actually about how to be a political gatekeeper or taste-maker through linguistic hand waving, and is not about developing models who better survive the rigors of being required to make real predictions about states of affairs.

romaniv 8y ago

>But then in a practical setting, the model doesn’t correspond to something physical or to the inference goal of a practitioner. How does this invalidate the notion of interpretability? A model can be both wrong/misapplied and fully interpretable.

mlthoughts2018 8y ago
> “How does this invalidate the notion of interpretability?” Who said that it did? I’m saying the development of a model that yields scientific progress doesn’t have to have a connection to the parent comment’s proposed definition of interpretability, and may have competing interpretability concerns driven by specific inference goals that have nothing to do with proofs about the model under assumptions.
- romaniv 8y ago
  >I’m saying the development of a model that yields scientific progress doesn’t have to have a connection to the parent comment’s proposed definition of interpretability Let's say someone used a neural network to predict planetary positions as a function of time, mass and so on. They made a network with several hundred parameters, trained until it stopped converging and published their final state vector. Would that ever lead to gravitational theory?
  - mlthoughts2018 8y ago
    What do you mean by “gravitational theory” apart from “correctly accounts for predicting the gravitational effects that we observe”? If a neural net can do that, then yes, a perfectly “elegant” theory could be the giant enumeration of a big ugly bunch of parameters. Of course we might suspect that’s overfitting and whittle down to a compact description, and that’s great, but doesn’t make the ugly enumeration of a big model any less scientific. Another point of view would be to say how does the Wiles proof of Fermat’s Last Theorem give us “understanding” (or substitute virtually any non-constructive existence proof, or proofs by contradiction, such as for the Halting Problem). Compact math descriptions are good, don’t get me wrong. When the mechanism of some data generating process is actually oriented in such a way that we can get a concise math description then we absolutely should. But that is largely unrelated to advancing understanding or scientific progress, which can perfectly be some ugly enumerated garble of parameters, or some extremely piecewise solution space. Not every data generating process is required to admit a concise mathematical description.