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# TODO: remove reference to laxy, clean up the code
############################
def sample_msa(samples=10000, burn_in=1, temp=1.0,
order=None, ar=False, diff=False, seq=True):
def sample_cat(key, logits=None, probs=None):
if logits is not None:
hard = jax.nn.one_hot(jax.random.categorical(key,logits/temp),logits.shape[-1])
probs = jax.nn.softmax(logits,-1)
elif probs is not None:
hard = (probs.cumsum(-1) >= jax.random.uniform(key, shape=probs.shape[:-1])).argmax(-1)
if diff: hard = jax.lax.stop_gradient(hard - probs) + probs
return hard
def sample_pll(key,msa,par):
N,L,A = msa.shape
if seq and ("w" in par or "mw" in par):
# sequential sampling
# burn_in = 1: autoregressive
# burn_in > 1: gibbs
def loop(m,x):
i,k = x
m_logits = []
if "w" in par: m_logits.append(jnp.einsum("njb,ajb->na", m, par["w"][i]))
if "b" in par: m_logits.append(par["b"][i])
if "mw" in par: m_logits.append(jnp.einsum("nc,njb,cajb->na", par["labels"], m, par["mw"][:,i]))
if "mb" in par: m_logits.append(jnp.einsum("nc,ca->na", par["labels"], par["mb"][:,i]))
return m.at[:,i].set(sample_cat(k,sum(m_logits))), None
# scan over positions
if order is not None: i = order
elif ar: i = jnp.arange(L)
else: i = jax.random.permutation(key,jnp.arange(L))
k = jax.random.split(key,L)
return jax.lax.scan(loop,msa,(i,k))[0]
else:
# sample all position independently
logits = []
if "b" in par: logits.append(par["b"])
if "mb" in par: logits.append(jnp.einsum("nc,cia->nia", par["labels"], par["mb"]))
if burn_in > 1:
if "w" in par: logits.append(jnp.einsum("njb,iajb->nia", msa, par["w"]))
if "mw" in par: logits.append(jnp.einsum("nc,njb,ciajb->nia", par["labels"], msa, par["mw"]))
return sample_cat(key,sum(logits))
def sample(key, params):
for p in ["b","w","mb","mw"]:
if p in params:
L,A = params[p].shape[-2:]
break
msa = jnp.zeros((samples,L,A))
# sample from mixture
if "c" in params and ("mb" in params or "mw" in params):
c = params["c"]
labels_logits = jnp.tile(c,(samples,1))
params["labels"] = jax.nn.one_hot(jax.random.categorical(key,labels_logits),c.shape[0])
if diff:
labels_soft = jax.nn.softmax(labels_logits,-1)
params["labels"] = jax.lax.stop_gradient(params["labels"] - labels_soft) + labels_soft
else:
params["labels"] = None
# number of iterations (burn-in)
sample_loop = lambda m,k:(sample_pll(k,m,params),None)
iters = jax.random.split(key,burn_in)
msa = jax.lax.scan(sample_loop,msa,iters)[0]
return {"msa":msa, "labels":params["labels"]}
return sample
def reg_loss(params, lam):
reg_loss = []
if "b" in params:
reg_loss.append(lam * jnp.square(params["b"]).sum())
if "w" in params:
L,A = params["w"].shape[-2:]
reg_loss.append(lam/2*(L-1)*(A-1) * jnp.square(params["w"]).sum())
if "mb" in params:
reg_loss.append(lam * jnp.square(params["mb"]).sum())
if "mw" in params:
L,A = params["mw"].shape[-2:]
reg_loss.append(lam/2*(L-1)*(A-1) * jnp.square(params["mw"]).sum())
return sum(reg_loss)
def pll_loss(params, inputs, order=None, labels=None):
logits = []
L = inputs["x"].shape[1]
w_mask = 1-jnp.eye(L)
if order is not None:
w_mask *= ar_mask(order)
if "b" in params:
logits.append(params["b"])
if "w" in params:
w = params["w"]
w = 0.5 * (w + w.transpose([2,3,0,1])) * w_mask[:,None,:,None]
logits.append(jnp.einsum("nia,iajb->njb", inputs["x"], w))
# MIXTURES
if "mb" in params:
logits.append(jnp.einsum("nc,cia->nia", labels, params["mb"]))
if "mw" in params:
mw = params["mw"]
mw = 0.5 * (mw + mw.transpose([0,3,4,1,2])) * w_mask[None,:,None,:,None]
logits.append(jnp.einsum("nc,nia,ciajb->njb", labels, inputs["x"], mw))
# categorical-crossentropy (or pseudo-likelihood)
cce_loss = -(inputs["x"] * jax.nn.log_softmax(sum(logits))).sum([1,2])
return (cce_loss*inputs["x_weight"]).sum()
class MRF:
def __init__(self, X, X_weight=None,
batch_size=None,
ar=False, ar_ent=False,
lam=0.01,
k=1, lr=0.1, shared=False, tied=True, full=False):
## MODE ##
inc = ["b","w"] if (tied or full) else ["b"]
if k > 1:
if shared:
if tied: inc += ["mb"]
if full: inc += ["mb","mw"]
else:
if tied: inc = ["mb","w"]
if full: inc = ["mb","mw"]
N,L,A = X.shape
self.batch_size = batch_size
self.k = k
# weight per sequence
X = jnp.asarray(X)
X_weight = get_eff(X) if X_weight is None else jnp.asarray(X_weight)
self.Neff = X_weight.sum()
if batch_size is None:
learning_rate = lr * np.log(N)/L
else:
lam = lam * batch_size/N
learning_rate = lr * jnp.log(batch_size)/L
if ar:
self.order = jnp.arange(L)
elif ar_ent:
f_i = (X * X_weight[:,None,None]).sum(0)/self.Neff
self.order = (-f_i * jnp.log(f_i + 1e-8)).sum(-1).argsort()
else:
self.order = None
# setup the model
def model(params, inputs):
labels = inputs["labels"] if "labels" in inputs else None
pll = pll_loss(params, inputs, self.order, labels)
reg = reg_loss(params, lam)
loss = pll + reg
return None, loss
# initialize inputs
self.inputs = {"x":X, "x_weight":X_weight}
# initialize params
self.params = {}
if "w" in inc: self.params["w"] = jnp.zeros((L,A,L,A))
if "mw" in inc: self.params["mw"] = jnp.zeros((k,L,A,L,A))
if "b" in inc:
b = jnp.log((X * X_weight[:,None,None]).sum(0) + (lam+1e-8) * jnp.log(self.Neff))
self.params["b"] = b - b.mean(-1,keepdims=True)
if "mb" in inc or "mw" in inc:
kms = kmeans(X, X_weight, k=k)
self.inputs["labels"] = kms["labels"]
mb = jnp.log(kms["means"] * self.Neff + (lam+1e-8) * jnp.log(self.Neff))
self.params["mb"] = mb - mb.mean(-1,keepdims=True)
if "b" in self.params:
self.params["mb"] -= self.params["b"]
# setup optimizer
self.opt = laxy.OPT(model, self.params, lr=learning_rate)
def get_msa(self, samples=1000, burn_in=1):
self.params = self.opt.get_params()
if "labels" in self.inputs:
self.params["c"] = jnp.log((self.inputs["x_weight"][:,None] * self.inputs["labels"]).sum(0) + 1e-8)
key = laxy.get_random_key()
return sample_msa(samples=samples,burn_in=burn_in,order=self.order)(key, self.params)
def get_w(self):
self.params = self.opt.get_params()
w = []
if "w" in self.params: w.append(self.params["w"])
if "mw" in self.params: w.append(self.params["mw"].sum(0))
w = sum(w)
w = (w + w.transpose(2,3,0,1))/2
w = w - w.mean((1,3),keepdims=True)
return w
def fit(self, steps=100, verbose=True, return_losses=False):
'''train model'''
losses = self.opt.fit(self.inputs, steps=steps, batch_size=self.batch_size,
verbose=verbose, return_losses=return_losses)
if return_losses: return losses
class MRF_BM:
def __init__(self, X, X_weight=None, samples=1000,
burn_in=1, temp=1.0,
ar=False, ar_ent=True,
lr=0.05, lam=0.01,
k=1, mode="tied"):
## MODE ##
inc = ["b","mb"] if k > 1 else ["b"]
if mode == "tied": inc += ["w"]
if mode == "full": inc += ["w","mw"] if k > 1 else ["w"]
self.X = jnp.asarray(X)
N,L,A = self.X.shape
learning_rate = lr * np.log(N)/L
# weight per sequence
self.X_weight = get_eff(X) if X_weight is None else jnp.asarray(X_weight)
self.Neff = self.X_weight.sum()
# collect stats
if k > 1:
self.kms = kmeans(self.X, self.X_weight, k=k)
self.labels = self.kms["labels"]
self.inputs = get_stats(self.X, self.X_weight, labels=self.kms["labels"],
add_mf_ij=("mw" in inc))
self.inputs["c"] = self.kms["cat"]
else:
self.labels = None
self.inputs = get_stats(self.X, self.X_weight)
# low entropy to high entropy
if ar_ent:
ent = -(self.inputs["f_i"] * jnp.log(self.inputs["f_i"] + 1e-8)).sum(-1)
self.order = ent.argsort()
elif ar: self.order = jnp.arange(L)
else: self.order = None
self.burn_in = burn_in
self.temp = temp
# setup the model
def model(params, inputs):
# sample msa
sample = sample_msa(samples=samples, burn_in=burn_in,
temp=temp, order=self.order)(inputs["key"], params)
# compute stats
stats = get_stats(sample["msa"], labels=sample["labels"],
add_mf_ij=("mw" in params))
# define gradients
grad = {}
I = (1-jnp.eye(L))[:,None,:,None]
if "c" in params: grad["c"] = sample["labels"].mean(0) - inputs["c"]
if "b" in params: grad["b"] = stats["f_i"] - inputs["f_i"]
if "w" in params: grad["w"] = (stats["f_ij"] - inputs["f_ij"]) * I
if "mb" in params: grad["mb"] = stats["mf_i"] - inputs["mf_i"]
if "mw" in params: grad["mw"] = (stats["mf_ij"] - inputs["mf_ij"]) * I[None]
# add regularization
reg_grad = jax.grad(reg_loss)(params,lam)
for g in grad.keys():
if g in reg_grad: grad[g] = grad[g] * self.Neff + reg_grad[g]
else: grad[g] = grad[g] * self.Neff
return None, None, grad
# initialize model params
self.params = {}
if "w" in inc:
self.params["w"] = jnp.zeros((L,A,L,A))
if "b" in inc:
b = jnp.log(self.inputs["f_i"] * self.Neff + (lam+1e-8) * jnp.log(self.Neff))
self.params["b"] = b - b.mean(-1,keepdims=True)
# setup mixture params
if "mb" in inc or "mw" in inc:
c = jnp.log(self.inputs["c"] * self.Neff + 1e-8)
self.params["c"] = c - c.mean(-1,keepdims=True)
if "mw" in inc:
self.params["mw"] = jnp.zeros((k,L,A,L,A))
if "mb" in inc:
mb = jnp.log(self.inputs["mf_i"] * self.Neff + (lam+1e-8) * jnp.log(self.Neff))
self.params["mb"] = mb - mb.mean(-1,keepdims=True)
if "b" in self.params: self.params["mb"] -= self.params["b"]
# setup optimizer
self.opt = laxy.OPT(model, self.params, lr=learning_rate, has_grad=True)
def get_msa(self, samples=1000, burn_in=None, temp=None, seed=0):
if burn_in is None: burn_in = self.burn_in
if temp is None: temp = self.temp
self.params = self.opt.get_params()
key = jax.random.PRNGKey(seed)
return sample_msa(samples=samples,
burn_in=self.burn_in,
order=self.order)(key, self.params)["msa"]
def fit(self, steps=1000, verbose=True):
'''train model'''
self.opt.fit(self.inputs, steps=steps, verbose=verbose) |