snr, matched filters and weight loss

One thing I keep hearing from weight/fat loss people is that you might as well only weigh yourself or check your body fat percentage once every week or two. The reasoning is that the signal is noisy: You can only lose weight/fat at a certain rate (and stay healthy), and hour-to-hour fluctuations in the amount of water and food just sitting in your body more or less swamp that rate. So it’s better to take your measurements at a rate that approximates the likely rate of change (at least if your plan is working).

This seems absolutely backwards to me. If you weigh yourself daily, any individual data point will be super-noisy, but you’ll get a good estimate of the real measurement and the real trend. If you weigh yourself weekly, and you happen to hit an outlier once, you can queer your whole trend, and thereby your whole understanding of where your weight is going in the medium term. Weighing yourself less frequently doesn’t reduce the noise.

The key insight, which everyone knows, is not to take any given measurement seriously. It’s possible the weight loss people know more than I do about human psychology — if you’re certain that one really bad or really good measurement will produce a bad outcome (e.g. depressive or triumphal bingeing), then you do want to reduce the chances of seeing one, which means reducing the number of measurements. To me, though, John Walker of the Hacker’s Diet has the right idea — record copious data, but guide your decisions with a smoothed time series rather than a raw one. (Despite having copious data, I have never actually implemented this strategy — partially because I tend to weigh myself at the gym, and I don’t go to the gym every day, and partially because I’m lazy.) But it does occur to me that there might be a quantitative justification for the sparse measurement regime in that it’s a crude matched filter. In fMRI analysis, we try to increase signal-to-noise ratio by smoothing the data using a function that we think corresponds to the spatial properties of the signal. Could sparse measurements at the presumptive time scale of weight loss actually improve the SNR of the measurement? It’s hard for me to believe — I’m conditioned to think that more data is always better, and in psychology that’s pretty much always true — but I’d be willing to hear arguments.


3 thoughts on “snr, matched filters and weight loss

  1. Nicely put. I’ve been using THD since early March, averaging slightly under a pound a week, and the filtering of noise is exactly the advantage you describe: I can be “over” any local minima for several days in a row, but I know to stay the course and not make drastic adjustments as long as the “trend” keeps coming down.

    I’m also a fan of THD because it measures the right thing; I don’t actually need to follow a “diet”, just keep weighing myself and using that as evidence of a net caloric deficit. (N.B. when you run as much as I do, weight loss is never as simple as dietary adjustments anyway.)

  2. Does the Hacker’s Diet really measure the right thing? I think most people are interested in fat loss in particular. But I guess you’re not going to lose much muscle as long as you’re exercising and not starving yourself.

  3. I suppose you’re right, that if you could accurately measure BF%, that might be more of what people are after, but mass is a metric people understand; nobody knows what their target BF% should be, they just think it should be “less.” (In fairness, most people think the same thing about weight, but whatever.)

    In my case, yes, exercise is part of the drill – THD just tells you what your calorie imbalance is, and you can tip that balance by burning more just as much as by eating less. And also, in my case, I’m a runner, and I know that I’m facing a pretty specific slowdown (2 seconds per pound per mile, all else being equal) which correlates directly to weight and not BF%. I also have a previous healthy benchmark I can compare to.

    (Which is not to say my present weight isn’t healthy; it’s just heavier, and given the choice of two healthy weights I’m going to run better at the lighter one.)

    (This is why runners look so skeletal: they don’t need that much muscle mass, and it takes losing a lot of it before it affects the “all else being equal” in the aside above.)

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