3 ms·

It's an idea about how to judge models. A model's predictive capabilities are modelled (indeed) as compression, like "how many bits do you need to set up your m

by tgv 3y ago

It's an idea about how to judge models. A model's predictive capabilities are modelled (indeed) as compression, like "how many bits do you need to set up your model and correct its output". It might be nice to compare fairly complete models on a well defined domain, but I can't see it as a general guiding principle. It would get theorizing stuck in a local minimum.

mjburgess 3y ago
Science isn't interested in this kind of prediction. That's just engineering. Causal models give counter-factual predictions for existence claims (eg., that a planet exists because the orbit of two other planets doesn't follow the causal model). Science, in most cases, prefers models with poor "engineering predictions" (ie., point estimates of observables) because they have vastly superior explanatory power. In most cases it would be a catastrophe for a scientific model to be making good estimates of observables, because we know a priori, that observables aren't fully determined by the model (eg., just consider that F=GMm/r^2 basically didnt apply to most observations of the solar system when it was formulated by newton; nor really does it much today). Explanatory power is not a property of compression, nor association, nor "prediction" in this engineering sense. Consider here that a lossless model of the solar system would never have yielded newton's law of graviton (since most of the objects in the solar system are unknown). This entire project is just, "what if science were like ML?" -- an interesting question only because how vast the gap is; and how absurd the suggestion.
- dr_dshiv 3y ago
  How can you tell the difference between a causal model and a predictive model? Isn’t it just the elegance of the model? And isn’t elegance just succinctness? Because another approach could focus on human comprehensibility. Indeed, a leading theory of scientific progress focuses on the advancement of noetic understanding. But, then we should really be irritated by things like quantum mechanics and love things like nutrition (we might get poor predictions but good understanding). I’m not sure myself.
  - mjburgess 3y ago
    No, it's a completely different semantics. F = GMm/r^2 does not mean anything about {P(F|M), P(F|m), ..) -- this this the semantics of associative statistical models, as used in ML. Rather it means a gravitational force is caused by the interaction of two masses over a distance r. Here `F` refers to a force via a scientific model, etc. The formula is a short-hand conceuqnece of a family of explanatory models about mass, inertia, gravity, forces, etc. and is only valid when used in the context of those models. Eg., you cannot equate F = GMm/r^2 to F = kQq/r^2. Not least since we have no gravitational model which applies to tiny charged particles. The formula used in scientific modelling do not have either mathematical or statistical semantics (ie., they dont refer to numbers, nor to associations). They refer to bits of the world via explanations; and are only valid insofar as these explanations apply. Though science seems obsessed by formula, in terms of the goal of science, it's the least important part of the scientific model. Explanations are the goal, and highly circumstantial consequences of these are given formula partly for illustration, partly for engineering. There's rarely anything in any dataset whose model would even be useful for building an explanation. Explanations are build via counter-factuals, and these are resolved by experimental data -- they are not made by it. Indeed, in many cases, the experimental data would be no where nearly modelled lossessly by the candidate hypothesis.
    - dr_dshiv 3y ago
      Here’s a toy example based on a project I’d like to do. I love faraday waves and Chladni plates — roughly speaking, cymatics. Now, if I record high res video of the waves on water in a dish, vibrating at different frequencies, I could likely create a diffusion model that had some latent “understanding” of the relationship between the proportional frequencies of sound and the waves in a particular sized dish. I could test this by holding out certain frequencies and observing whether the diffusion model could recreate them. So, I can ask the question of whether the AI model learned wave physics. Here, there would be no formula, per se, and no explanation. Merely a computational model that could make predictions about physical phenomena. Now, what makes this less scientific than a formula and set of explanations for the experiments? Is it because I can relate the the explanations linguistically to everything else I know about science? So, in that case, If I jointly developed a language model to do the same thing as the diffusion model, ie make predictions based on data—but linguistically capable of connecting the outcomes to scientific concepts, then would then it be scientific?

by tgv 3y ago

mjburgess 3y ago

Science isn't interested in this kind of prediction. That's just engineering. Causal models give counter-factual predictions for existence claims (eg., that a planet exists because the orbit of two other planets doesn't follow the causal model). Science, in most cases, prefers models with poor "engineering predictions" (ie., point estimates of observables) because they have vastly superior explanatory power. In most cases it would be a catastrophe for a scientific model to be making good estimates of observables, because we know a priori, that observables aren't fully determined by the model (eg., just consider that F=GMm/r^2 basically didnt apply to most observations of the solar system when it was formulated by newton; nor really does it much today). Explanatory power is not a property of compression, nor association, nor "prediction" in this engineering sense. Consider here that a lossless model of the solar system would never have yielded newton's law of graviton (since most of the objects in the solar system are unknown). This entire project is just, "what if science were like ML?" -- an interesting question only because how vast the gap is; and how absurd the suggestion.

dr_dshiv 3y ago
How can you tell the difference between a causal model and a predictive model? Isn’t it just the elegance of the model? And isn’t elegance just succinctness? Because another approach could focus on human comprehensibility. Indeed, a leading theory of scientific progress focuses on the advancement of noetic understanding. But, then we should really be irritated by things like quantum mechanics and love things like nutrition (we might get poor predictions but good understanding). I’m not sure myself.
- mjburgess 3y ago
  No, it's a completely different semantics. F = GMm/r^2 does not mean anything about {P(F|M), P(F|m), ..) -- this this the semantics of associative statistical models, as used in ML. Rather it means a gravitational force is caused by the interaction of two masses over a distance r. Here `F` refers to a force via a scientific model, etc. The formula is a short-hand conceuqnece of a family of explanatory models about mass, inertia, gravity, forces, etc. and is only valid when used in the context of those models. Eg., you cannot equate F = GMm/r^2 to F = kQq/r^2. Not least since we have no gravitational model which applies to tiny charged particles. The formula used in scientific modelling do not have either mathematical or statistical semantics (ie., they dont refer to numbers, nor to associations). They refer to bits of the world via explanations; and are only valid insofar as these explanations apply. Though science seems obsessed by formula, in terms of the goal of science, it's the least important part of the scientific model. Explanations are the goal, and highly circumstantial consequences of these are given formula partly for illustration, partly for engineering. There's rarely anything in any dataset whose model would even be useful for building an explanation. Explanations are build via counter-factuals, and these are resolved by experimental data -- they are not made by it. Indeed, in many cases, the experimental data would be no where nearly modelled lossessly by the candidate hypothesis.
  - dr_dshiv 3y ago
    Here’s a toy example based on a project I’d like to do. I love faraday waves and Chladni plates — roughly speaking, cymatics. Now, if I record high res video of the waves on water in a dish, vibrating at different frequencies, I could likely create a diffusion model that had some latent “understanding” of the relationship between the proportional frequencies of sound and the waves in a particular sized dish. I could test this by holding out certain frequencies and observing whether the diffusion model could recreate them. So, I can ask the question of whether the AI model learned wave physics. Here, there would be no formula, per se, and no explanation. Merely a computational model that could make predictions about physical phenomena. Now, what makes this less scientific than a formula and set of explanations for the experiments? Is it because I can relate the the explanations linguistically to everything else I know about science? So, in that case, If I jointly developed a language model to do the same thing as the diffusion model, ie make predictions based on data—but linguistically capable of connecting the outcomes to scientific concepts, then would then it be scientific?