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<!DOCTYPE html>
<html>
<head>
<title>Learning</title>
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<textarea id="source">
### Lifelong Learning: <br>Theory and Practice and Coresets
PI: Joshua T. Vogelstein, [JHU](https://www.jhu.edu/) <br>
Co-PI: Vova Braverman, [JHU](https://www.jhu.edu/) <br>
Jayanta Dey, Will LeVine, Hayden Helm, Ali Geisa, Ronak Mehta,
Carey E. Priebe
<!-- | Joshua T. Vogelstein <br> -->
<!-- [Microsoft Research](https://www.microsoft.com/en-us/research/): Weiwei Yang | Jonathan Larson | Bryan Tower | Chris White -->
---
### How does our LL approach work?
1. We learn representations independently for each task
2. We ensemble the representations both past and future tasks
3. We illustrate it achieves SOTA forward & backward transfer on CIFAR 10x10 and Microsoft language tasks
4. It can be applied to any sequential task-aware classification task
---
### Key Innovations
1. Modernized statistical decision theory to explicitly incorporate a .ye[learning task]
2. Introduced .ye[learning efficiency]
3. Formalized and unified .ye[learning metrics]
4. Identified .ye[partition & vote] equivalence of Deep Networks and Decision Forests
5. Developed .ye[Progressive Learning Forests and Networks]
6. Illustrated the value of .ye[coresets] for lifelong learning (vova)
---
### Learning Task Definition
| Component | Notation | Examples |
| :--- | :--- | :---
| Query Space | $\mathcal{Q}$ | is this a cat?
| Action Space | $\mathcal{A}$ | A,B, ←, →, ↑, ↓
| Measurement Space | $\mathcal{Z}$ | 8-bit images, 256 x 256
| Statistical Model | $\mathcal{P}$ | Gaussian
| Hypotheses | $\mathcal{H}$ | linear classifiers
| Risk | $R$ | expected loss
| Algorithm Space | $\mathcal{F}$ | Random Forests
| True & Unknown Distribution | $P$ | $\mu=0$, $\sigma=1$
---
### What is learning?
.ye[$f$] learns from .ye[data] $\mathbf{Z}_n$ with respect to .ye[task] $t$ when its .ye[performance] at $t$ improves due to $\mathbf{Z}_n$.
- Define .ye[generalization error] $\mathcal{E}_n(f) := \mathbb{E}_P[R(f(\bold{Z}_n))]$
- $\bold{Z}_0$ corresponds to no data.
- Define .ye[learning efficiency]: $$LE_n(f) :=
\frac{\mathbb{E}_P[R(f(\bold{Z}_0))]}{\mathbb{E}_P[R(f(\bold{Z}_n))]} =
\frac{\mathcal{E}_0(f)}{\mathcal{E}_n(f)}$$
<br>
$f$ learns from $\mathbf{Z}_n$ with respect to task $t$ when $LE_n(f) > 1$.
---
### What is forward learning?
- Let $n\_t$ be the last occurence of task $t$ in $\mathbf{Z}\_n$
- Let $\mathbf{Z}\_n^{< t} = \lbrace Z\_1, Z\_2, \ldots, Z\_{n_t} \rbrace$
.ye[Forward] learning efficiency is the improvement on task $t$ resulting from all data .ye[preceding] task $t$
$$FL^t\_{\mathbf{n}}(f) := \frac{\mathbb{E}[R^t(f(\mathbf{Z}^{t}\_n))]}{\mathbb{E}[R^t(f(\mathbf{Z}^{< t}\_n))]} =\frac{\mathcal{E}\_{Z\_n^t}(f)}{\mathcal{E}\_{Z\_n^{< t}}(f)}.$$
<br>
$f$ .ye[forward learns] if $FL_{\mathbf{n}}(f) > 1$.
---
### What is backward learning?
.ye[Backward] learning efficiency is the improvement on task $t$ resulting from all data .ye[after] task $t$
$$ BL^t\_{\mathbf{n}}(f) := \frac{\mathbb{E}[R^t(f(\mathbf{Z}^{< t}\_n))]}{\mathbb{E}[R^t(f(\mathbf{Z}\_n))]} =\frac{\mathcal{E}\_{Z\_n^{< t}}(f)}{\mathcal{E}\_{Z\_n}(f)}. $$
<br>
$f$ .ye[backward learns] if $BL_{\mathbf{n}}(f) > 1$.
---
### Unification of Learning Metrics
Each of the previous definitions are all special cases of $LE^t(\mathbf{Z}\_A, \mathbf{Z}\_B; f)$, for specific choices of $\mathbf{Z}\_A$ and $\mathbf{Z}\_B$
- Learning: $\mathbf{Z}\_A=\mathbf{Z}\_0$ and $\mathbf{Z}\_B=\mathbf{Z}\_n$.
- Transfer learning: $\mathbf{Z}\_A=\mathbf{Z}\_n^t$ and $\mathbf{Z}\_B=\mathbf{Z}\_n$.
- Multitask learning: for each $t$, $\mathbf{Z}\_A=\mathbf{Z}\_n^t$ and $\mathbf{Z}\_B=\mathbf{Z}\_n$.
- Forward learning: $\mathbf{Z}\_A=\mathbf{Z}\_n^t$ and $\mathbf{Z}\_B=\mathbf{Z}\_n^{< t}$.
- Backward learning: $\mathbf{Z}\_A=\mathbf{Z}\_n^{< t}$ and $\mathbf{Z}\_B=\mathbf{Z}\_n$.
Conjecture: All learning metrics we care about are functions of learning efficiency for a specific $\mathbf{Z}\_A$ and $\mathbf{Z}\_B$.
---
### Deep Nets and Decision Forests
- Both learn convex polytope partitions of feature space, with affine activation functions
- We can easily swap between the two empirically and theoretically
---
#### Progressive Learning Forests and Networks
1. Representers can be forest, networks, etc.
1. Seperate representers learned for each task
2. Voters leverage both past and future representers
---
### Key Strength
- SOTA forward transfer
- Unique backward transfer using 500 training samples (SOTA)
- Monotonically increasing backward transfer (SOTA)
---
### Key Limitations
1. Only works for task-aware (not task-unaware)
1. Only works for classification (not regression)
2. Only batched data (not streaming, not RL)
3. Theorems not yet with dotted i's and crossed t's
---
---
---
### Acknowledgements
<!-- <div class="small-container">
<img src="faces/ebridge.jpg"/>
<div class="centered">Eric Bridgeford</div>
</div>
<div class="small-container">
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<div class="centered">Ben Pedigo</div>
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</div>
##### JHU
<div class="small-container">
<img src="faces/cep.png"/>
<div class="centered">Carey Priebe</div>
</div>
<!-- <div class="small-container">
<img src="faces/randal.jpg"/>
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</div> -->
<!-- <div class="small-container">
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</div> -->
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<!-- <div class="small-container">
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</div> -->
<!-- <div class="small-container">
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</div>
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<div class="centered">Drishti Mannan</div>
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<!-- <div class="small-container">
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<!-- <div class="small-container">
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<div class="centered">Benjamin Falk</div>
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<!-- <div class="small-container">
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<div class="centered">Kwame Kutten</div>
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<div class="centered">Eric Perlman</div>
</div> -->
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<div class="centered">Alex Loftus</div>
</div> -->
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<div class="centered">Brian Caffo</div>
</div> -->
<!-- <div class="small-container">
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<div class="centered">Minh Tang</div>
</div> -->
<!-- <div class="small-container">
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<div class="centered">Avanti Athreya</div>
</div> -->
<!-- <div class="small-container">
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<div class="centered">Vince Lyzinski</div>
</div> -->
<!-- <div class="small-container">
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<div class="centered">Daniel Sussman</div>
</div> -->
<!-- <div class="small-container">
<img src="faces/youngser.jpg"/>
<div class="centered">Youngser Park</div>
</div> -->
<!-- <div class="small-container">
<img src="faces/shangsi.jpg"/>
<div class="centered">Shangsi Wang</div>
</div> -->
<!-- <div class="small-container">
<img src="faces/tyler.jpg"/>
<div class="centered">Tyler Tomita</div>
</div> -->
<!-- <div class="small-container">
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<div class="centered">James Brown</div>
</div> -->
<!-- <div class="small-container">
<img src="faces/disa.jpg"/>
<div class="centered">Disa Mhembere</div>
</div> -->
<!-- <div class="small-container">
<img src="faces/gkiar.jpg"/>
<div class="centered">Greg Kiar</div>
</div> -->
<!-- <div class="small-container">
<img src="faces/jeremias.png"/>
<div class="centered">Jeremias Sulam</div>
</div> -->
<div class="small-container">
<img src="faces/meghana.png"/>
<div class="centered">Meghana Madhya</div>
</div>
<!-- <div class="small-container">
<img src="faces/percy.png"/>
<div class="centered">Percy Li</div>
</div>
-->
<div class="small-container">
<img src="faces/ronak.jpg"/>
<div class="centered">Ronak Mehta</div>
</div>
<div class="small-container">
<img src="faces/jayanta.jpg"/>
<div class="centered">Jayanta Dey</div>
</div>
<div class="small-container">
<img src="faces/will.jpg"/>
<div class="centered">Will LeVine</div>
</div>
<div class="small-container">
<img src="faces/hayden.png"/>
<div class="centered">Hayden Helm</div>
</div>
<div class="small-container">
<img src="faces/rguo.jpg"/>
<div class="centered">Richard Gou</div>
</div>
<div class="small-container">
<img src="faces/alig.jpg"/>
<div class="centered">Ali Geisa</div>
</div>
##### Microsoft Research
<div class="small-container">
<img src="faces/chwh-180x180.jpg"/>
<div class="centered">Chris White</div>
</div>
<div class="small-container">
<img src="faces/weiwei.jpg"/>
<div class="centered">Weiwei Yang</div>
</div>
<div class="small-container">
<img src="faces/jolarso150px.png"/>
<div class="centered">Jonathan Larson</div>
</div>
<div class="small-container">
<img src="faces/brtower-180x180.jpg"/>
<div class="centered">Bryan Tower</div>
</div>
##### DARPA L2M: All code open source and reproducible from [proglearn.neurodata.io/](http://proglearn.neurodata.io/)
<!-- Hava, Ben, Robert, Jennifer, Ted. -->
{[BME](https://www.bme.jhu.edu/),[CIS](http://cis.jhu.edu/), [ICM](https://icm.jhu.edu/), [KNDI](http://kavlijhu.org/)}@[JHU](https://www.jhu.edu/) | [neurodata](https://neurodata.io)
<br>
[jovo@jhu.edu](mailto:[email protected]) | <http://neurodata.io/talks> | [@neuro_data](https://twitter.com/neuro_data)
</div>
<!-- <img src="images/funding/nsf_fpo.png" STYLE="HEIGHT:95px;"/> -->
<!-- <img src="images/funding/nih_fpo.png" STYLE="HEIGHT:95px;"/> -->
<!-- <img src="images/funding/darpa_fpo.png" STYLE=" HEIGHT:95px;"/> -->
<!-- <img src="images/funding/iarpa_fpo.jpg" STYLE="HEIGHT:95px;"/> -->
<!-- <img src="images/funding/KAVLI.jpg" STYLE="HEIGHT:95px;"/> -->
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---
background-image: url(images/l_and_v.jpeg)
.footnote[Questions?]
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